Zeitschriftenartikel zum Thema „Chen system“

A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole ℝ3using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.

This paper addresses the synchronization problem of two modified Chen systems in the presence of unknown system parameters. One-way coupling and active control laws are applied to achieve the state synchronization of two identical modified Chen systems. Based on Lyapunov stability theory, active control laws are derived such that the two modified Chen systems are to be synchronized. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.

This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.

In this paper, the research of the Jacobi stability of the Chen system is performed by using the KCC-theory. By associating a nonlinear connection and a Berwald connection, five geometrical invariants of the Chen system are obtained. The Jacobi stability of the Chen system at equilibrium points and a periodic orbit is investigated in terms of the eigenvalues of the deviation curvature tensor. The obtained results show that the origin is always Jacobi unstable, while the Jacobi stability of the other two nonzero equilibrium points depends on the values of the parameters. And a periodic orbit of the Chen system is proved to be also Jacobi unstable. Furthermore, Jacobi stability regions of the Chen system and the Lorenz system are compared. Finally, the dynamical behavior of the components of the deviation vector near the equilibrium points is also discussed.

This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

This paper presents a novel unified hyperchaotic system that contains the hyperchaotic Lorenz system and the hyperchaotic Chen system as two dual systems at the two extremes of its parameter spectrum. The new system is hyperchaotic over almost the whole range of the system parameter and continuously transfers from the hyperchaotic Lorenz system to the hyperchaotic Chen system. The new findings are not only demonstrated by computer simulations but also verified with bifurcation analysis, Lyapunov exponents and Lyapunov dimension.

The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and between integer-order hyperchaotic Chen system and fractional-order hyperchaotic Rössler system is used to illustrate the effectiveness of the proposed synchronization approach. Numerical simulations coincide with the theoretical analysis.

In this paper, we study chaos control of the fractional order Chen system with the bounded random parameter. Firstly, we transform the fractional order Chen system with random parameter into an equivalent deterministic system by the orthogonal polynomial approximation. Secondly, based on Routh-Hrwitz criterion, the derivative feedback control laws are applied to fractional order equivalent deterministic Chen system. Lastly, numerical simulations show that the control method is effective and feasible.

In this article, three-dimensional autonomous chaotic systems with two quadratic terms, similar to the Lorenz system in their algebraic forms, are studied. An attractor with two clearly distinguishable scrolls similar to the Lorenz attractor is referred to as a Lorenz-like attractor, while an attractor with more intertwine between the two scrolls similar to the Chen attractor is referred to as a Chen-like attractor. A gallery of Lorenz-like attractors and Chen-like attractors are presented. For several different families of such systems, through tuning only one real parameter gradually, each of them can generate a spectrum of chaotic attractors continuously changing from a Lorenz-like attractor to a Chen-like attractor. Some intrinsic relationships between the Lorenz system and the Chen system are revealed and discussed. Some common patterns of the Lorenz-like and Chen-like attractors are found and analyzed, which suggest that the instability of the two saddle-foci of such a system somehow determines the shape of its chaotic attractor. These interesting observations on the general dynamic patterns hopefully could shed some light for a better understanding of the intrinsic relationships between the algebraic structures and the geometric attractors of these kinds of chaotic systems.

Solving the linear first-order Partial Differential Equations (PDEs) derived from the unified Lorenz system, it is found that there is a unified Hamiltonian (energy function) for the Lorenz and Chen systems, and the unified energy function shows a hyperboloid of one sheet for the Lorenz system and an ellipsoidal surface for the Chen system in three-dimensional phase space, which can be used to explain that the Lorenz system is not equivalent to the Chen system. Using the unified energy function, we obtain two generalized Hamiltonian realizations of these two chaotic systems, respectively. Moreover, the energy function and generalized Hamiltonian realization of the Lü system and a four-dimensional hyperchaotic Lorenz-type system are also discussed.

This article addresses the adaptive synchronization problem of two Chen systems with uncertain parameters. Two adaptive synchronization methods are designed. In the two methods, we use only two controllers to synchronize uncertain Chen systems. It is theoretically proved that these two methods can make uncertain Chen systems asymptotically synchronized and identify the unknown parameters. Numerical simulations show the effectiveness of the proposed methods further. The comparisons of these two methods show: The method of theorem 1 is easier and more feasible than that of theorem 2, and the synchronization results are better.

This paper shows that a large class of systems, introduced in [Čelikovský & Vaněček, 1994; Vaněček & Čelikovský, 1996] as the so-called generalized Lorenz system, are state-equivalent to a special canonical form that covers a broader class of chaotic systems. This canonical form, called generalized Lorenz canonical form hereafter, generalizes the one introduced and analyzed in [Čelikovský & Vaněček, 1994; Vaněček & Čelikovský, 1996], and also covers the so-called Chen system, recently introduced in [Chen & Ueta, 1999; Ueta & Chen, 2000].Thus, this new generalized Lorenz canonical form contains as special cases the original Lorenz system, the generalized Lorenz system, and the Chen system, so that a comparison of the structures between two essential types of chaotic systems becomes possible. The most important property of the new canonical form is the parametrization that has precisely a single scalar parameter useful for chaos tuning, which has promising potential in future engineering chaos design. Some other closely related topics are also studied and discussed in the paper.

A new network data transmission strategy was proposed in [Zhang & Chen, 2005], where the resulting nonlinear system was analyzed and the effectiveness of the transmission strategy was demonstrated via simulations. In this paper, we further generalize the results of Zhang and Chen [2005] in the following ways: (1) Construct first-return maps of the nonlinear systems formulated in [Zhang & Chen, 2005] and derive several existence conditions of periodic orbits and study their properties. (2) Formulate the new system as a hybrid system, which will ease the succeeding analysis. (3) Prove that this type of hybrid systems is not structurally stable based on phase transition which can be applied to higher-dimensional cases effortlessly. (4) Simulate a higher-dimensional model with emphasis on their rich dynamics. (5) Study a class of continuous-time hybrid systems as the counterparts of the discrete-time systems discussed above. (6) Propose new controller design methods based on this network data transmission strategy to improve the performance of each individual system and the whole network. We hope that this research and the problems posed here will rouse the interest of researchers in such fields as control, dynamical systems and numerical analysis.

This paper introduces a new practical method for distinguishing chaotic, periodic and quasi-periodic orbits based on a new criterion, and apply it to investigate the local bifurcations of the Chen system. Conditions for supercritical and subcritical bifurcations are obtained, with their parameter domains specified. The analytic results are also verified by numerical simulation studies.

In this paper, the first new chaotic system is gained by anti-controlling Chen system,which belongs to the general Lorenz system; also, the second new chaotic system is gained by anti-controlling the first new chaotic system, which belongs to the general Lü system. Moreover,some basic dynamical properties of two new chaotic systems are studied, either numerically or analytically. The obtained results show clearly that Chen chaotic system and two new chaotic systems also can form another Lorenz system family and deserve further detailed investigation.

This paper investigates the global chaos synchronization of identical Liu-Su-Liu chaotic systems (2006) and non-identical Liu-Su-Liu chaotic system (2006) and Liu-Chen-Liu chaotic system (2007). In this paper, active nonlinear control method has been successfully applied to synchronize two identical Liu-Su-Liu chaotic systems and then to synchronize two different chaotic systems, viz. Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Since the Lyapunov exponents are not required for these calculations, the active nonlinear control method is effective and convenient to synchronize Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Numerical simulations are also given to illustrate the proposed synchronization approach.

This letter reports an interesting finding that the parametric Lorenz system and the parametric Chen system "shake hands" at a particular point of their common parameter space, as the time variable t → +∞ in the Lorenz system while t → -∞ in the Chen system. This helps better clarify and understand the relationship between these two closely related but topologically nonequivalent chaotic systems.

This paper reports the finding of a simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. By tuning the only parameter, this system can continuously generate a variety of cascading Lorenz-like attractors, which appears to be richer than the unified chaotic system that contains the Lorenz and the Chen systems as its two extremes. Although this new family of chaotic systems has very rich and complex dynamics, it has a very simple algebraic structure with only two quadratic terms (same as the Lorenz and the Chen systems) and all nonzero coefficients in the linear part being -1 except one -0.1 (thus, simpler than the Lorenz and Chen systems). Surprisingly, although this new system belongs to the Lorenz-type of systems in the classification of the generalized Lorenz canonical form, it can generate not only Lorenz-like attractors but also Chen-like attractors. This suggests that there may exist some other unknown yet more essential algebraic characteristics for describing general three-dimensional quadratic autonomous chaotic systems.

This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), particle swarm optimization (PSO), and invasive weed optimization (IWO). In each algorithm, the optimization process is performed using 100 individuals and generations from 50 to 500, with a step of 50, which makes a total of ten independent runs. The results show that the optimized fractional order chaotic Chen systems have higher maximum Lyapunov exponents than the non-optimized system, with the DE giving the highest MLE. Additionally, the results indicate that the chaotic behavior of the fractional order Chen system is multifaceted with respect to the parameter and fractional order values. The dynamical behavior and complexity of the optimized systems are verified using properties, such as bifurcation, LE spectrum, equilibrium point, eigenvalue, and sample entropy. Moreover, the optimized systems are compared with a hyper-chaotic Chen system on the basis of their prediction times. The results show that the optimized systems have a shorter prediction time than the hyper-chaotic system. The optimized results are suitable for developing a secure communication system and a random number generator. Finally, the Halstead parameters measure the complexity of the three optimization algorithms that were implemented in MATLAB. The results reveal that the invasive weed optimization has the simplest implementation.

A modified generalized Lorenz system in a canonical form extended from the generalized Lorenz system is proposed in this paper. This novel system has a folded factor and can display complex 2-scroll folded attractors and 1-scroll folded attractors at different parameter values. Three typical normal forms, called Lorenz-like, Chen-like and Lü-like chaotic system respectively, of three-dimensional quadratic autonomous chaotic systems are derived, and their dynamical behaviors are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincaré mapping and phase portrait, etc. Of particular interest is the fact that the folded factor makes Chen-like and Lü-like chaotic systems exhibit complicated nonlinear dynamical phenomena.

We focus on the two-dimensional stable manifold of Chen system. Based on the Chen system, a new system with nonlinear control is put forward, which exhibits brand new dynamical phenomena such as the coexistence of heteroclinic orbits with periodic solutions, or two new attractors. The emergence of manifold surface is found by tangential self-intersection. The two-dimensional unstable manifold of saddle-focus tends to another equilibrium solution asymptotically, the underlying heteroclinic bifurcation and the “twins” unstable manifolds are bulit from two saddle-focus respectively.

Wang–Chen system with only one stable equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one stable equilibrium to hidden attractors without equilibrium.

In this paper, we investigate the chaotic behaviors of the Chen system with Caputo–Hadamard derivative. First, we construct some practical numerical schemes for the Chen system with Caputo–Hadamard derivative. Then, by means of the variational equation, we estimate the bounds of the Lyapunov exponents for the considered system. Furthermore, we analyze the dynamical evolution of the Chen system with Caputo–Hadamard derivative based on the Lyapunov exponents, and we found that chaos does exist in the considered system. Some phase diagrams and Lyapunov exponent spectra are displayed to verify our analysis.

This letter reports a study on some topological properties of chaos using a generalized competitive mode (GCM). The Lorenz system and the Chen system are used as examples for comparison. It is shown that for typical parameter values used in the two systems, the Lorenz attractor has one pair of GCMs in competition, while the Chen attractor has two pairs of GCMs in competition. This explains why the two attractors are topologically different, and furthermore indicates that the Chen attractor is more complex than the Lorenz attractor from the dynamics point of view.

In 2013 the Editor of Journal of Vibration and Control and SAGE became aware of a peer review ring involving assumed and fabricated identities that appeared to centre around Peter Chen at National Pingtung University of Education, Taiwan (NPUE). SAGE and the Editor then began a complex investigation into the case during the rest of 2013 and 2014. Following an unsatisfactory response from Peter Chen, NPUE was notified. NPUE were serious in addressing the Journal and SAGE’s concerns. NPUE confirmed that the institution was investigating Peter Chen. SAGE subsequently uncovered a citation ring involving the above mentioned author and others. We regret that individual authors have compromised the academic record by perverting the peer review process and apologise to readers. On uncovering problems with peer review and citation SAGE immediately put steps in place to avoid similar vulnerability of the Journal to exploitation in the future. More information may be found at www.sagepub.co.uk/JVC_Statement_2014 . The Journal and SAGE understand from NPUE that Peter Chen has resigned his post at NPUE. The following articles are retracted because after thorough investigation evidence points towards them having at least one author or being reviewed by at least one reviewer who has been implicated in the peer review ring and/or citation ring. All authors have had an opportunity to respond to the allegations and proposed actions. OnlineFirst articles (these articles will not be published in an issue) Chen CY, Chen T-H, Chen Y-H, Yu S-E and Chung P-Y (2013) Information technology system modeling an integrated C-TAM-TPB model to the validation of ocean tidal analyses Journal of Vibration and Control Epub ahead of print 7 May 2013. doi: 10.1177/1077546312472924 Chang R-F, Chen CY, Su F-P and Lin H-C (2013) A two-step approach for broadband digital signal processing technique Journal of Vibration and Control Epub ahead of print 26 April 2013. doi: 10.1177/1077546312472925 Chen TH, Chang CJ, Yu SE, Chung PY and Liu C-K (2013) Nonlinear information analysis and system management technique: the influence of design experience and control complexity Journal of Vibration and Control Epub ahead of print 12 April 2013. doi: 10.1177/1077546312473321 Chen CY, Shih BY, Chen YH, Yu SE and Liu YC (2013) The exploration of a 3T flow model using vibrating NXT: II. Model validation Journal of Vibration and Control Epub ahead of print 10 April 2013. doi: 10.1177/1077546312470481 Chen CY, Shih BY, Chen YH, Yu SE and Liu YC (2013) The exploration of 3T flow model using vibrating NXT: I. model formulation Journal of Vibration and Control Epub ahead of print 6 February 2013. doi: 10.1177/1077546312467360 Lin M-L and Chen C-W (2013) Stability analysis of fuzzy-based NN modeling for ecosystems using fuzzy Lyapunov methods Journal of Vibration and Control Epub ahead of print 6 February 2013. doi: 10.1177/1077546312466687 Chen CY, Chen TH, Chen YH and Chiu J (2012) A multi-stage method for deterministic-statistical analysis: a mathematical case and measurement studies Journal of Vibration and Control Epub ahead of print 20 December 2012. doi: 10.1177/1077546312466579 Shih BY, Lin MC and Chen CY (2012) Autonomous navigation system for radiofrequency identification mobile robot e-book reader Journal of Vibration and Control Epub ahead of print 13 December 2012. doi: 10.1177/1077546312466578 Chang RF, Chen CY, Su FP, Lin HC and Lu C-K (2012) Multiphase SUMO robot based on an agile modeling-driven process for a small mobile robot Journal of Vibration and Control Epub ahead of print 13 December 2012. doi: 10.1177/1077546312464993 Shih B-Y, Lin Y-K, Cheng M-H, Chen C-Y and Chiu C-P (2012) The development of an application program interactive game-based information system Journal of Vibration and Control Epub ahead of print 12 December 2012. doi: 10.1177/1077546312464682 Chen C-Y, Chang C-J and Lin C-H (2012) On dynamic access control in web 2.0 and cloud interactive information hub: technologies Journal of Vibration and Control Epub ahead of print 12 December 2012. doi: 10.1177/1077546312464992 Shin BY, Chen CY and Hsu KH (2012) Robot cross platform system using innovative interactive theory and selection algorithms for Android application Journal of Vibration and Control Epub ahead of print 13 November 2012. doi: 10.1177/1077546312463757 Articles published in an issue Chen C-W (2014) Applications of neural-network-based fuzzy logic control to a nonlinear time-delay chaotic system Journal of Vibration and Control 20 (4): 589-605. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312461370 Chen C-W (2014) A review of intelligent algorithm approaches and neural-fuzzy stability criteria for time-delay tension leg platform systems Journal of Vibration and Control 20 (4): 561-575. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312463759 Chen C-Y, Chang C-J and Lin C-H (2014) On dynamic access control in web 2.0 and cloud interactive information hub: trends and theories Journal of Vibration and Control 20 (4): 548-560. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312463762 Lin M-L and Chen C-W (2014) Stability conditions for ecosystem modeling using the fuzzy Lyapunov method Journal of Vibration and Control 20 (2): 290-302. Epub ahead of print 23 October 2012. doi: 10.1177/1077546312451301 Chen C-H, Kuo C-M, Hsieh S-H and Chen C-Y (2014) Highly efficient very-large-scale integration (VLSI) implementation of probabilistic neural network image interpolator Journal of Vibration and Control 20 (2): 218-224. Epub ahead of print 22 October 2012. doi: 10.1177/1077546312458822 Chen C-Y (2014) Wave vibration and simulation in dissipative media described by irregular boundary surfaces: a mathematical formulation Journal of Vibration and Control 20 (2): 191-203. Epub ahead of print 22 October 2012. doi: 10.1177/1077546312464258 Chen C-H, Yao T-K, Dai J-H and Chen C-Y (2014) A pipelined multiprocessor system- on-a-chip (SoC) design methodology for streaming signal processing Journal of Vibration and Control 20 (2): 163-178. Epub ahead of print 16 October 2012. doi: 10.1177/1077546312458821 Lin M-L and Chen C-W (2014) Fuzzy neural modeling for n-degree ecosystems using the linear matrix inequality approach Journal of Vibration and Control 20 (1): 82-93. Epub ahead of print 8 October 2012. doi: 10.1177/1077546312458533 Chen C-H, Wu W-X and Chen C-Y (2013) Ant-inspired collective problem-solving systems Journal of Vibration and Control 19 (16): 2481-2490. Epub ahead of print 18 September 2012. doi: 10.1177/1077546312456231 Chen C-H, Yao T-K, Kuo C-M and Chen C-Y (2013) Evolutionary design of constructive multilayer feedforward neural network Journal of Vibration and Control 19 (16): 2413-2420. Epub ahead of print 12 September 2012. doi: 10.1177/1077546312456726 Chen C-W (2013) Applications of the fuzzy-neural Lyapunov criterion to multiple time-delay systems Journal of Vibration and Control 19 (13): 2054-2067. Epub ahead of print 16 August 2012. doi: 10.1177/1077546312451034 Chung P-Y, Chen Y-H, Walter L and Chen C-Y (2013) Influence and dynamics of a mobile robot control on mechanical components Journal of Vibration and Control 19 (13): 1923-1935. Epub ahead of print 20 July 2012. doi: 10.1177/1077546312452184 Chen C-W (2013) Neural network-based fuzzy logic parallel distributed compensation controller for structural system Journal of Vibration and Control 19 (11): 1709-1727. Epub ahead of print 22 June 2012. doi: 10.1177/1077546312442233 Chen C-W, Yeh K, Yang H-C, Liu KFR and Liu C-C (2013) A critical review of structural system control by the large-scaled neural network linear-deferential-inclusion-based criterion Journal of Vibration and Control 19 (11): 1658-1673. Epub ahead of print 18 June 2012. doi: 10.1177/1077546312443377 Chen C-H, Kuo C-M, Chen C-Y and Dai J-H (2013) The design and synthesis using hierarchical robotic discrete-event modeling Journal of Vibration and Control 19 (11): 1603-1613. Epub ahead of print 27 June 2012. doi: 10.1177/1077546312449645 Chang CJ, Chen CY and Chou I-T (2013) The design of information and communication technologies: telecom MOD strength machines Journal of Vibration and Control 19 (10): 1499-1513. Epub ahead of print 27 June 2012. doi: 10.1177/1077546312449644 Shih B-Y, Chen C-Y, Li K-H, Wu T-Y, Chen G-Y (2013) A novel NXT control method for implementing force sensing and recycling in a training robot Journal of Vibration and Control 19 (10): 1443-1459. Epub ahead of print 1 June 2012. doi: 10.1177/1077546312446361 Chen C-W, Chen P-C and Chiang W-L (2013) Modified intelligent genetic algorithm-based adaptive neural network control for uncertain structural systems Journal of Vibration and Control 19 (9): 1333-1347. Epub ahead of print 31 May 2012. doi: 10.1177/1077546312442232 Chen C-Y, Shih B-Y, Shih C-H and Wang L-H (2013) Enhancing robust and stability control of a humanoid biped robot: system identification approach. Journal of Vibration and Control 19 (8): 1199-1207. Epub ahead of print 26 April 2012. doi: 10.1177/1077546312442947 Chang C-J, Chen C-Y and Huang C-W (2013) Applications for medical recovery using wireless control of a bluetooth ball with a hybrid G-sensor and human-computer interface technology Journal of Vibration and Control 19 (8): 1139-1151. Epub ahead of print 24 April 2012. doi: 10.1177/1077546312442948 Hsu W-K, Chiou D-J, Chen C-W, Liu M-Y, Chiang W-L and Huang P-C (2013) Sensitivity of initial damage detection for steel structures using the Hilbert-Huang transform method Journal of Vibration and Control 19 (6): 857-878. Epub ahead of print 29 February 2012. doi: 10.1177/1077546311434794 Chen C-Y, Shih B-Y, Shih C-H and Wang L-H (2013) Human–machine interface for the motion control of humanoid biped robots using a graphical user interface Motion Editor Journal of Vibration and Control 19 (6): 814-820. Epub ahead of print 23 February 2012. doi: 10.1177/1077546312437804 Chen C-Y (2013) Internal wave transport, nonlinear manifestation, and mixing in a stratified shear layer - technical briefs Journal of Vibration and Control 19 (3): 429-438. Epub ahead of print 18 January 2012. doi: 10.1177/1077546311429337 Chen C-W (2013) Delay independent criterion for multiple time-delay systems and its application in building structure control systems Journal of Vibration and Control 19 (3): 395-414. Epub ahead of print 17 January 2012. doi: 10.1177/1077546311429341 Chen C-Y, Shih B-Y, Shih C-H and Wang L-H (2013) Design, modeling and stability control for an actuated dynamic walking planar bipedal robot Journal of Vibration and Control 19 (3): 376-384. Epub ahead of print 17 January 2012. doi: 10.1177/1077546311429476 Liu K-C, Liu Y-W, Chen C-Y and Huang W-C (2013) Nonlinear vibration of structural deterioration in reinforced concrete columns: experimental and theoretical investigation Journal of Vibration and Control 19 (3): 323-335. Epub ahead of print 17 January 2012. doi: 10.1177/1077546311429477 Chen C-Y, Shih B-Y and Ma J-m (2013) Development for low-cost and cross-platform robot control environment Journal of Vibration and Control 19 (2): 228-233. Epub ahead of print 11 January 2012. doi: 10.1177/1077546311430107 Shih B-Y, Chang H and Chen C-Y (2013) Path planning for autonomous robots – a comprehensive analysis by a greedy algorithm Journal of Vibration and Control 19 (1): 130-142. Epub ahead of print 17 January 2012. doi: 10.1177/1077546311429841 Liu T-Y, Chiang W-L, Chen C-W, Hsu W-K, Lin C-W, Chiou D-J and Huang P-C (2012) Structural system identification for vibration bridges using the Hilbert–Huang transform Journal of Vibration and Control 18 (13): 1939-1956. Epub ahead of print 14 December 2011. doi: 10.1177/1077546311428347 Chen C-W (2012) Applications of the fuzzy Lyapunov linear matrix inequality criterion to a chaotic structural system Journal of Vibration and Control 18 (13): 1925-1938. Epub ahead of print 14 December 2011. doi: 10.1177/1077546311428346 Chen C-W (2012) Applications of linear differential inclusion-based criterion to a nonlinear chaotic system: a critical review Journal of Vibration and Control 18 (12): 1886-1899. Epub ahead of print 14 December 2011. doi: 10.1177/1077546311428345 Shih B-Y, Chen C-Y and Chou W (2012) An enhanced obstacle avoidance and path correction mechanism for an autonomous intelligent robot with multiple sensors Journal of Vibration and Control 18 (12): 1855-1864. Epub ahead of print 14 December 2011. doi: 10.1177/1077546311426734 Chen C-W, Yeh K, Liu KFR and Lin M-L (2012) Applications of fuzzy control to nonlinear time-delay systems using the linear matrix inequality fuzzy Lyapunov method Journal of Vibration and Control 18 (10): 1561-1574. Epub ahead of print 18 October 2011. doi: 10.1177/1077546311410765 Chen C-Y (2012) A critical review of internal wave dynamics. Part 2 – Laboratory experiments and theoretical physics Journal of Vibration and Control 18 (7): 983-1008. Epub ahead of print 21 September 2011. doi: 10.1177/1077546310397561 Chen C-Y and Huang P-H (2012) Review of an autonomous humanoid robot and its mechanical control Journal of Vibration and Control 18 (7): 973-982. Epub ahead of print 21 September 2011. doi: 10.1177/1077546310395974 Shih B-Y, Chen C-Y, Chang H and Ma J-m (2012) Dynamics and control for robotic manipulators using a greedy algorithm approach Journal of Vibration and Control 18 (6): 859-866. Epub ahead of print 25 August 2011. doi: 10.1177/1077546311407649 Yeh K, Chen C-W, Lo DC and Liu KFR (2012) Neural-network fuzzy control for chaotic tuned mass damper systems with time delays Journal of Vibration and Control 18 (6): 785-795. Epub ahead of print 15 August 2011. doi: 10.1177/1077546311407538 Chen C-Y, Shih B-Y, Shih C-H and Chou W-C (2012) The development of autonomous low-cost biped mobile surveillance robot by intelligent bricks Journal of Vibration and Control 18 (5): 577-586. Epub ahead of print 21 April 2011. doi: 10.1177/1077546310371349 Chen C-Y (2012) A critical review of internal wave dynamics. Part 1 – Remote sensing and in-situ observations Journal of Vibration and Control 18 (3): 417-436. Epub ahead of print 13 July 2011. doi: 10.1177/1077546310395971 Tseng C-P, Chen C-W and Liu KFR (2012) Risk control allocation model for pressure vessels and piping project Journal of Vibration and Control 18 (3): 385-394. Epub ahead of print 13 July 2011. doi: 10.1177/1077546311403182 Lin M-L and Chen C-W (2011) Stability analysis of community and ecosystem hierarchies using the Lyapunov method Journal of Vibration and Control 17 (13): 1930-1937. Epub ahead of print 9 December 2010. doi: 10.1177/1077546310385737 Chen C-Y, Shih B-Y, Chou W-C, Li Y-J and Chen Y-H (2011) Obstacle avoidance design for a humanoid intelligent robot with ultrasonic sensors Journal of Vibration and Control 17 (12): 1798-1804. Epub ahead of print 26 November 2010. doi: 10.1177/1077546310381101 Chen C-W (2011) Fuzzy control of interconnected structural systems using the fuzzy Lyapunov method Journal of Vibration and Control 17 (11): 1693-1702. Epub ahead of print 23 November 2010. doi: 10.1177/1077546310379625 Shih B-Y, Chen C-Y and Chou W-C (2011) Obstacle avoidance using a path correction method for autonomous control of a biped intelligent robot Journal of Vibration and Control 17 (10): 1567-1573. Epub ahead of print 22 November 2010. doi: 10.1177/1077546310372004 Tang J-P, Chiou D-J, Chen C-W, Chiang W-L, Hsu W-K, Chen C-Y and Liu T-Y (2011) A case study of damage detection in benchmark buildings using a Hilbert-Huang Transform-based method Journal of Vibration and Control 17 (4): 623-636. Epub ahead of print 8 November 2010. doi: 10.1177/1077546309360053 Liu TY, Chiang WL, Chen CW, Hsu WK, Lu LC and Chu TJ (2011) Identification and monitoring of bridge health from ambient vibration data Journal of Vibration and Control 17 (4): 589-603. Epub ahead of print 12 November 2010. doi: 10.1177/1077546309360049 Lin JW, Huang CW, Shih CH and Chen CY (2011) Fuzzy Lyapunov Stability Analysis and NN Modeling for Tension Leg Platform Systems Journal of Vibration and Control 17 (1): 151-158. Epub ahead of print 25 August 2010. doi: 10.1177/1077546309350477 Lee WI, Chen CY, Kuo HM and Sui YC (2010) The Development of Half-circle Fuzzy Numbers and Application in Fuzzy Control Journal of Vibration and Control 16 (13): 1977-1987. Epub ahead of print 22 April 2010. doi: 10.1177/1077546309349849

In 2013 the Editor of Journal of Vibration and Control and SAGE became aware of a peer review ring involving assumed and fabricated identities that appeared to centre around Peter Chen at National Pingtung University of Education, Taiwan (NPUE). SAGE and the Editor then began a complex investigation into the case during the rest of 2013 and 2014. Following an unsatisfactory response from Peter Chen, NPUE was notified. NPUE were serious in addressing the Journal and SAGE’s concerns. NPUE confirmed that the institution was investigating Peter Chen. SAGE subsequently uncovered a citation ring involving the above mentioned author and others. We regret that individual authors have compromised the academic record by perverting the peer review process and apologise to readers. On uncovering problems with peer review and citation SAGE immediately put steps in place to avoid similar vulnerability of the Journal to exploitation in the future. More information may be found at www.sagepub.co.uk/JVC_Statement_2014 . The Journal and SAGE understand from NPUE that Peter Chen has resigned his post at NPUE. The following articles are retracted because after thorough investigation evidence points towards them having at least one author or being reviewed by at least one reviewer who has been implicated in the peer review ring and/or citation ring. All authors have had an opportunity to respond to the allegations and proposed actions. OnlineFirst articles (these articles will not be published in an issue) Chen CY, Chen T-H, Chen Y-H, Yu S-E and Chung P-Y (2013) Information technology system modeling an integrated C-TAM-TPB model to the validation of ocean tidal analyses Journal of Vibration and Control Epub ahead of print 7 May 2013. doi: 10.1177/1077546312472924 Chang R-F, Chen CY, Su F-P and Lin H-C (2013) A two-step approach for broadband digital signal processing technique Journal of Vibration and Control Epub ahead of print 26 April 2013. doi: 10.1177/1077546312472925 Chen TH, Chang CJ, Yu SE, Chung PY and Liu C-K (2013) Nonlinear information analysis and system management technique: the influence of design experience and control complexity Journal of Vibration and Control Epub ahead of print 12 April 2013. doi: 10.1177/1077546312473321 Chen CY, Shih BY, Chen YH, Yu SE and Liu YC (2013) The exploration of a 3T flow model using vibrating NXT: II. Model validation Journal of Vibration and Control Epub ahead of print 10 April 2013. doi: 10.1177/1077546312470481 Chen CY, Shih BY, Chen YH, Yu SE and Liu YC (2013) The exploration of 3T flow model using vibrating NXT: I. model formulation Journal of Vibration and Control Epub ahead of print 6 February 2013. doi: 10.1177/1077546312467360 Lin M-L and Chen C-W (2013) Stability analysis of fuzzy-based NN modeling for ecosystems using fuzzy Lyapunov methods Journal of Vibration and Control Epub ahead of print 6 February 2013. doi: 10.1177/1077546312466687 Chen CY, Chen TH, Chen YH and Chiu J (2012) A multi-stage method for deterministic-statistical analysis: a mathematical case and measurement studies Journal of Vibration and Control Epub ahead of print 20 December 2012. doi: 10.1177/1077546312466579 Shih BY, Lin MC and Chen CY (2012) Autonomous navigation system for radiofrequency identification mobile robot e-book reader Journal of Vibration and Control Epub ahead of print 13 December 2012. doi: 10.1177/1077546312466578 Chang RF, Chen CY, Su FP, Lin HC and Lu C-K (2012) Multiphase SUMO robot based on an agile modeling-driven process for a small mobile robot Journal of Vibration and Control Epub ahead of print 13 December 2012. doi: 10.1177/1077546312464993 Shih B-Y, Lin Y-K, Cheng M-H, Chen C-Y and Chiu C-P (2012) The development of an application program interactive game-based information system Journal of Vibration and Control Epub ahead of print 12 December 2012. doi: 10.1177/1077546312464682 Chen C-Y, Chang C-J and Lin C-H (2012) On dynamic access control in web 2.0 and cloud interactive information hub: technologies Journal of Vibration and Control Epub ahead of print 12 December 2012. doi: 10.1177/1077546312464992 Shin BY, Chen CY and Hsu KH (2012) Robot cross platform system using innovative interactive theory and selection algorithms for Android application Journal of Vibration and Control Epub ahead of print 13 November 2012. doi: 10.1177/1077546312463757 Articles published in an issue Chen C-W (2014) Applications of neural-network-based fuzzy logic control to a nonlinear time-delay chaotic system Journal of Vibration and Control 20 (4): 589-605. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312461370 Chen C-W (2014) A review of intelligent algorithm approaches and neural-fuzzy stability criteria for time-delay tension leg platform systems Journal of Vibration and Control 20 (4): 561-575. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312463759 Chen C-Y, Chang C-J and Lin C-H (2014) On dynamic access control in web 2.0 and cloud interactive information hub: trends and theories Journal of Vibration and Control 20 (4): 548-560. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312463762 Lin M-L and Chen C-W (2014) Stability conditions for ecosystem modeling using the fuzzy Lyapunov method Journal of Vibration and Control 20 (2): 290-302. Epub ahead of print 23 October 2012. doi: 10.1177/1077546312451301 Chen C-H, Kuo C-M, Hsieh S-H and Chen C-Y (2014) Highly efficient very-large-scale integration (VLSI) implementation of probabilistic neural network image interpolator Journal of Vibration and Control 20 (2): 218-224. Epub ahead of print 22 October 2012. doi: 10.1177/1077546312458822 Chen C-Y (2014) Wave vibration and simulation in dissipative media described by irregular boundary surfaces: a mathematical formulation Journal of Vibration and Control 20 (2): 191-203. Epub ahead of print 22 October 2012. doi: 10.1177/1077546312464258 Chen C-H, Yao T-K, Dai J-H and Chen C-Y (2014) A pipelined multiprocessor system- on-a-chip (SoC) design methodology for streaming signal processing Journal of Vibration and Control 20 (2): 163-178. Epub ahead of print 16 October 2012. doi: 10.1177/1077546312458821 Lin M-L and Chen C-W (2014) Fuzzy neural modeling for n-degree ecosystems using the linear matrix inequality approach Journal of Vibration and Control 20 (1): 82-93. Epub ahead of print 8 October 2012. doi: 10.1177/1077546312458533 Chen C-H, Wu W-X and Chen C-Y (2013) Ant-inspired collective problem-solving systems Journal of Vibration and Control 19 (16): 2481-2490. Epub ahead of print 18 September 2012. doi: 10.1177/1077546312456231 Chen C-H, Yao T-K, Kuo C-M and Chen C-Y (2013) Evolutionary design of constructive multilayer feedforward neural network Journal of Vibration and Control 19 (16): 2413-2420. Epub ahead of print 12 September 2012. doi: 10.1177/1077546312456726 Chen C-W (2013) Applications of the fuzzy-neural Lyapunov criterion to multiple time-delay systems Journal of Vibration and Control 19 (13): 2054-2067. Epub ahead of print 16 August 2012. doi: 10.1177/1077546312451034 Chung P-Y, Chen Y-H, Walter L and Chen C-Y (2013) Influence and dynamics of a mobile robot control on mechanical components Journal of Vibration and Control 19 (13): 1923-1935. Epub ahead of print 20 July 2012. doi: 10.1177/1077546312452184 Chen C-W (2013) Neural network-based fuzzy logic parallel distributed compensation controller for structural system Journal of Vibration and Control 19 (11): 1709-1727. Epub ahead of print 22 June 2012. doi: 10.1177/1077546312442233 Chen C-W, Yeh K, Yang H-C, Liu KFR and Liu C-C (2013) A critical review of structural system control by the large-scaled neural network linear-deferential-inclusion-based criterion Journal of Vibration and Control 19 (11): 1658-1673. Epub ahead of print 18 June 2012. doi: 10.1177/1077546312443377 Chen C-H, Kuo C-M, Chen C-Y and Dai J-H (2013) The design and synthesis using hierarchical robotic discrete-event modeling Journal of Vibration and Control 19 (11): 1603-1613. Epub ahead of print 27 June 2012. doi: 10.1177/1077546312449645 Chang CJ, Chen CY and Chou I-T (2013) The design of information and communication technologies: telecom MOD strength machines Journal of Vibration and Control 19 (10): 1499-1513. Epub ahead of print 27 June 2012. doi: 10.1177/1077546312449644 Shih B-Y, Chen C-Y, Li K-H, Wu T-Y, Chen G-Y (2013) A novel NXT control method for implementing force sensing and recycling in a training robot Journal of Vibration and Control 19 (10): 1443-1459. Epub ahead of print 1 June 2012. doi: 10.1177/1077546312446361 Chen C-W, Chen P-C and Chiang W-L (2013) Modified intelligent genetic algorithm-based adaptive neural network control for uncertain structural systems Journal of Vibration and Control 19 (9): 1333-1347. Epub ahead of print 31 May 2012. doi: 10.1177/1077546312442232 Chen C-Y, Shih B-Y, Shih C-H and Wang L-H (2013) Enhancing robust and stability control of a humanoid biped robot: system identification approach. Journal of Vibration and Control 19 (8): 1199-1207. Epub ahead of print 26 April 2012. doi: 10.1177/1077546312442947 Chang C-J, Chen C-Y and Huang C-W (2013) Applications for medical recovery using wireless control of a bluetooth ball with a hybrid G-sensor and human-computer interface technology Journal of Vibration and Control 19 (8): 1139-1151. Epub ahead of print 24 April 2012. doi: 10.1177/1077546312442948 Hsu W-K, Chiou D-J, Chen C-W, Liu M-Y, Chiang W-L and Huang P-C (2013) Sensitivity of initial damage detection for steel structures using the Hilbert-Huang transform method Journal of Vibration and Control 19 (6): 857-878. Epub ahead of print 29 February 2012. doi: 10.1177/1077546311434794 Chen C-Y, Shih B-Y, Shih C-H and Wang L-H (2013) Human–machine interface for the motion control of humanoid biped robots using a graphical user interface Motion Editor Journal of Vibration and Control 19 (6): 814-820. Epub ahead of print 23 February 2012. doi: 10.1177/1077546312437804 Chen C-Y (2013) Internal wave transport, nonlinear manifestation, and mixing in a stratified shear layer - technical briefs Journal of Vibration and Control 19 (3): 429-438. Epub ahead of print 18 January 2012. doi: 10.1177/1077546311429337 Chen C-W (2013) Delay independent criterion for multiple time-delay systems and its application in building structure control systems Journal of Vibration and Control 19 (3): 395-414. Epub ahead of print 17 January 2012. doi: 10.1177/1077546311429341 Chen C-Y, Shih B-Y, Shih C-H and Wang L-H (2013) Design, modeling and stability control for an actuated dynamic walking planar bipedal robot Journal of Vibration and Control 19 (3): 376-384. Epub ahead of print 17 January 2012. doi: 10.1177/1077546311429476 Liu K-C, Liu Y-W, Chen C-Y and Huang W-C (2013) Nonlinear vibration of structural deterioration in reinforced concrete columns: experimental and theoretical investigation Journal of Vibration and Control 19 (3): 323-335. Epub ahead of print 17 January 2012. doi: 10.1177/1077546311429477 Chen C-Y, Shih B-Y and Ma J-m (2013) Development for low-cost and cross-platform robot control environment Journal of Vibration and Control 19 (2): 228-233. Epub ahead of print 11 January 2012. doi: 10.1177/1077546311430107 Shih B-Y, Chang H and Chen C-Y (2013) Path planning for autonomous robots – a comprehensive analysis by a greedy algorithm Journal of Vibration and Control 19 (1): 130-142. Epub ahead of print 17 January 2012. doi: 10.1177/1077546311429841 Liu T-Y, Chiang W-L, Chen C-W, Hsu W-K, Lin C-W, Chiou D-J and Huang P-C (2012) Structural system identification for vibration bridges using the Hilbert–Huang transform Journal of Vibration and Control 18 (13): 1939-1956. Epub ahead of print 14 December 2011. doi: 10.1177/1077546311428347 Chen C-W (2012) Applications of the fuzzy Lyapunov linear matrix inequality criterion to a chaotic structural system Journal of Vibration and Control 18 (13): 1925-1938. Epub ahead of print 14 December 2011. doi: 10.1177/1077546311428346 Chen C-W (2012) Applications of linear differential inclusion-based criterion to a nonlinear chaotic system: a critical review Journal of Vibration and Control 18 (12): 1886-1899. Epub ahead of print 14 December 2011. doi: 10.1177/1077546311428345 Shih B-Y, Chen C-Y and Chou W (2012) An enhanced obstacle avoidance and path correction mechanism for an autonomous intelligent robot with multiple sensors Journal of Vibration and Control 18 (12): 1855-1864. Epub ahead of print 14 December 2011. doi: 10.1177/1077546311426734 Chen C-W, Yeh K, Liu KFR and Lin M-L (2012) Applications of fuzzy control to nonlinear time-delay systems using the linear matrix inequality fuzzy Lyapunov method Journal of Vibration and Control 18 (10): 1561-1574. Epub ahead of print 18 October 2011. doi: 10.1177/1077546311410765 Chen C-Y (2012) A critical review of internal wave dynamics. Part 2 – Laboratory experiments and theoretical physics Journal of Vibration and Control 18 (7): 983-1008. Epub ahead of print 21 September 2011. doi: 10.1177/1077546310397561 Chen C-Y and Huang P-H (2012) Review of an autonomous humanoid robot and its mechanical control Journal of Vibration and Control 18 (7): 973-982. Epub ahead of print 21 September 2011. doi: 10.1177/1077546310395974 Shih B-Y, Chen C-Y, Chang H and Ma J-m (2012) Dynamics and control for robotic manipulators using a greedy algorithm approach Journal of Vibration and Control 18 (6): 859-866. Epub ahead of print 25 August 2011. doi: 10.1177/1077546311407649 Yeh K, Chen C-W, Lo DC and Liu KFR (2012) Neural-network fuzzy control for chaotic tuned mass damper systems with time delays Journal of Vibration and Control 18 (6): 785-795. Epub ahead of print 15 August 2011. doi: 10.1177/1077546311407538 Chen C-Y, Shih B-Y, Shih C-H and Chou W-C (2012) The development of autonomous low-cost biped mobile surveillance robot by intelligent bricks Journal of Vibration and Control 18 (5): 577-586. Epub ahead of print 21 April 2011. doi: 10.1177/1077546310371349 Chen C-Y (2012) A critical review of internal wave dynamics. Part 1 – Remote sensing and in-situ observations Journal of Vibration and Control 18 (3): 417-436. Epub ahead of print 13 July 2011. doi: 10.1177/1077546310395971 Tseng C-P, Chen C-W and Liu KFR (2012) Risk control allocation model for pressure vessels and piping project Journal of Vibration and Control 18 (3): 385-394. Epub ahead of print 13 July 2011. doi: 10.1177/1077546311403182 Lin M-L and Chen C-W (2011) Stability analysis of community and ecosystem hierarchies using the Lyapunov method Journal of Vibration and Control 17 (13): 1930-1937. Epub ahead of print 9 December 2010. doi: 10.1177/1077546310385737 Chen C-Y, Shih B-Y, Chou W-C, Li Y-J and Chen Y-H (2011) Obstacle avoidance design for a humanoid intelligent robot with ultrasonic sensors Journal of Vibration and Control 17 (12): 1798-1804. Epub ahead of print 26 November 2010. doi: 10.1177/1077546310381101 Chen C-W (2011) Fuzzy control of interconnected structural systems using the fuzzy Lyapunov method Journal of Vibration and Control 17 (11): 1693-1702. Epub ahead of print 23 November 2010. doi: 10.1177/1077546310379625 Shih B-Y, Chen C-Y and Chou W-C (2011) Obstacle avoidance using a path correction method for autonomous control of a biped intelligent robot Journal of Vibration and Control 17 (10): 1567-1573. Epub ahead of print 22 November 2010. doi: 10.1177/1077546310372004 Tang J-P, Chiou D-J, Chen C-W, Chiang W-L, Hsu W-K, Chen C-Y and Liu T-Y (2011) A case study of damage detection in benchmark buildings using a Hilbert-Huang Transform-based method Journal of Vibration and Control 17 (4): 623-636. Epub ahead of print 8 November 2010. doi: 10.1177/1077546309360053 Liu TY, Chiang WL, Chen CW, Hsu WK, Lu LC and Chu TJ (2011) Identification and monitoring of bridge health from ambient vibration data Journal of Vibration and Control 17 (4): 589-603. Epub ahead of print 12 November 2010. doi: 10.1177/1077546309360049 Lin JW, Huang CW, Shih CH and Chen CY (2011) Fuzzy Lyapunov Stability Analysis and NN Modeling for Tension Leg Platform Systems Journal of Vibration and Control 17 (1): 151-158. Epub ahead of print 25 August 2010. doi: 10.1177/1077546309350477 Lee WI, Chen CY, Kuo HM and Sui YC (2010) The Development of Half-circle Fuzzy Numbers and Application in Fuzzy Control Journal of Vibration and Control 16 (13): 1977-1987. Epub ahead of print 22 April 2010. doi: 10.1177/1077546309349849

An experimental secure communication method based on the Chen system with time-delay is being proposed in this paper. The Chen system with time-delay is an infinite-dimensional system having more than one positive Lyapunov exponent. The message to be transmitted is encrypted using an hyperchaotic signal generated by the Chen system with time-delay and multishift cipher function. This encryption makes difficult for an eavesdropper to reconstruct the attractor by using time-delay embedding techniques, return map reconstruction, or spectral analysis, consequently, improving the security. Simulations and experiments on TI TMS320C6713 Digital Signal Processor (DSP) show improved resilience against attack and the feasibility of the proposed scheme.

We investigate chaos control nodes of the complex network synchronization. The structure of the coupling functions between the connected nodes is obtained based on the chaos control method and Lyapunov stability theory. Moreover a complex network with nodes of the new unified Loren-Chen-Lü system, Coullet system, Chee-Lee system, and the New system is taken as an example; numerical simulations are used to verify the effectiveness of the method.

This paper presents the Chen system as a controlled weather model. Mathematically, the Chen system is dual to the Lorenz system via time reversal. Physically, the Chen system can be viewed as a controlled weather model from the anti-control perspective. This paper illustrates the physical principle of this controlled weather model, and develops an engineering design of the model for real indoor climate (temperature-humidity) regulation, with a perspective on outdoor weather control application.

This work investigates chaos synchronization between two different fractional order chaotic systems of Lorenz family. The fractional order Lü system is controlled to be the fractional order Chen system, and the fractional order Chen system is controlled to be the fractional order Lorenz-like system. The analytical conditions for the synchronization of these pairs of different fractional order chaotic systems are derived by utilizing Laplace transform. Numerical simulations are used to verify the theoretical analysis using different values of the fractional order parameter.

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

The Chen system of equations exhibits Lorenz, Transition, Chen and Transverse 8 type of chaotic attractors depending on the system parameters. Some authors have proposed a generalized competitive mode (GCM) technique to explain the topological difference between the Lorenz attractor and the Chen attractor. In this paper, we show a range of parameter values for which the nature of the topological attractor for the Chen system is not in accordance with that expected from GCM analysis. Instead, we find that return maps can be used to characterize the transition between different types of attractors more reliably.

This paper presents two novel synchronization schemes for Chen chaotic system, drive-response synchronization and adaptive synchronization with unknown parameters, numerical simulation results demonstrate the effectiveness of the proposed method.

We study the stochastically forced Chen system in its parameter zone under the transition to chaos via period-doubling bifurcations. We suggest a stochastic sensitivity function technique for the analysis of stochastic cycles. We show that this approach allows to construct the dispersion ellipses of random trajectories for any Poincaré sections, and these ellipses reflect the essential features of a spatial arrangement of random trajectories near deterministic cycles. For the Chen system, we demonstrate a growth of stochastic sensitivity of the forced cycles under transition to chaos.

In this article, we investigate the generation of a class of hyperchaotic systems via the Chen chaotic system using both integer order and fractional order differential equation systems. Based on the Chen chaotic system, we designed a system with four nonlinear ordinary differential equations. For different parameter sets, the trajectory of the system may diverge or display a hyperchaotic attractor with double wings. By linearizing the ordinary differential equation system with divergent trajectory and designing proper switching controls, we obtain a chaotic attractor. Similar phenomenon has also been observed in linearizing the hyperchaotic system. The corresponding fractional order systems are also considered. Our investigation indicates that, switching control can be applied to either linearized chaotic or nonchaotic differential equation systems to create chaotic attractor.

In this paper, chaos synchronization is studied. Two schemes are proposed to synchronizing Chen chaotic system with all the system parameters unknown. Especially in the last two schemes, only one state variable is contained in the controller. Also, numerical simulations are given to illustrate the effectiveness of the methods.