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Journal articles on the topic 'Multi-scroll chaotic attractor'

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Published: 4 June 2021

Last updated: 1 February 2022

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1

Vaidyanathan, Sundarapandian, Aceng Sambas, Mohamad Afendee Mohamed, Mustafa Mamat, W. S. Mada Sanjaya, and Sudarno Sudarno. "A new 2-D multi-stable chaotic attractor and its MultiSim electronic circuit design." Indonesian Journal of Electrical Engineering and Computer Science 22, no. 2 (May 1, 2021): 699. http://dx.doi.org/10.11591/ijeecs.v22.i2.pp699-707.

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<span>A new multi-stable system with a double-scroll chaotic attractor is developed in this paper. Signal plots are simulated using MATLAB and multi-stability is established by showing two different coexisting double-scroll chaotic attractors for different states and same set of parameters. Using integral sliding control, synchronized chaotic attractors are achieved between drive-response chaotic attractors. A MultiSim circuit is designed for the new chaotic attractor, which is useful for practical engineering realizations.</span>

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2

LIU, XINZHI, XUEMIN SHERMAN SHEN, and HONGTAO ZHANG. "MULTI-SCROLL CHAOTIC AND HYPERCHAOTIC ATTRACTORS GENERATED FROM CHEN SYSTEM." International Journal of Bifurcation and Chaos 22, no. 02 (February 2012): 1250033. http://dx.doi.org/10.1142/s0218127412500332.

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In this paper, we create a multi-scroll chaotic attractor from Chen system by a nonlinear feedback control. The dynamic behavior of the new chaotic attractor is analyzed. Specially, the Lyapunov spectrum and Lyapunov dimension are calculated and the bifurcation diagram is sketched. Furthermore, via changing the value of the control parameters, we can increase the number of equilibrium points and obtain a family of more complex chaotic attractors with different topological structures. By introducing time delay to the feedback control, we then generalize the multi-scroll attractor to a set of hyperchaotic attractors. Computer simulations are given to illustrate the phase portraits with different system parameters.

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3

Yin, Wen Shuang, Dai Jun Wei, and Shi Qiang Chen. "A Novel Four-Order Chaotic System with N-Attractor Multi-Direction Multi-Scroll Attractors." Applied Mechanics and Materials 678 (October 2014): 81–88. http://dx.doi.org/10.4028/www.scientific.net/amm.678.81.

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In this paper, a novel four-order system is proposed. It can generate N-attractor multi-direction multi-scroll attractor by adding simple nonlinear functions. We analyze the new system by using means of maximum Lyapunov exponent, bifurcation diagram and Poincaré maps of the system. Moreover, an minimum operational amplifier circuit is designed for realizing 2×(3×3 ×3) scroll chaotic attractors, and experimental results are also obtained, which verify chaos characteristics of the system.

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4

Sampath, Sivaperumal, Sundarapandian Vaidyanathan, Aceng Sambas, Mohamad Afendee, Mustafa Mamat, and Mada Sanjaya. "A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation." International Journal of Engineering & Technology 7, no. 3 (August 24, 2018): 1931. http://dx.doi.org/10.14419/ijet.v7i3.14865.

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This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.

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5

Huang, Yong. "A New Grid Multi-Scroll Chaotic System and the Simulation Based on Labview." Advanced Materials Research 538-541 (June 2012): 2666–69. http://dx.doi.org/10.4028/www.scientific.net/amr.538-541.2666.

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In order to get the grid Multi-Scroll in the two directions, based on a simple unstable system, the way of the combination of the translational transform and step function was put forward to make the scrolls extending in the x and y directions in this paper. The quantity of scrolls can be controlled by two parameters N and M. A simulation system was designed with Labview to simulate grid Multi-Scroll chaotic system, it demonstrates the existence of grid Multi-Scroll chaotic attractor.

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6

YU, SIMIN, WALLACE K. S. TANG, JINHU LÜ, and GUANRONG CHEN. "DESIGN AND IMPLEMENTATION OF MULTI-WING BUTTERFLY CHAOTIC ATTRACTORS VIA LORENZ-TYPE SYSTEMS." International Journal of Bifurcation and Chaos 20, no. 01 (January 2010): 29–41. http://dx.doi.org/10.1142/s0218127410025387.

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Lorenz system, as the first classical chaotic system, has been intensively investigated over the last four decades. Based on the sawtooth wave function, this paper initiates a novel approach for generating multi-wing butterfly chaotic attractors from the generalized first and second kinds of Lorenz-type systems. Compared with the traditional ring-shaped multi-scroll Lorenz chaotic attractors, the proposed multi-wing butterfly chaotic attractors are much easier to be designed and implemented by analog circuits. The dynamical behaviors of these multi-wing butterfly chaotic systems are further studied. Theoretical analysis shows that every index-2 saddle-focus equilibrium corresponds to a unique wing in the butterfly attractors. Finally, a module-based unified circuit diagram is constructed for realizing various multi-wing butterfly attractors. It should be especially pointed out that this is the first time in the literature that a maximal 10-wing butterfly chaotic attractor is experimentally verified by analog circuits.

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7

HU, GUOSI, and BO YU. "A HYPERCHAOTIC SYSTEM WITH A FOUR-WING ATTRACTOR." International Journal of Modern Physics C 20, no. 02 (February 2009): 323–35. http://dx.doi.org/10.1142/s0129183109013649.

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Recently, there are many methods for constructing multi-wing/multi-scroll or hyperchaotic attractors; however, it has been noticed that the attractors with both multi-wing topological structure and hyperchaotic characteristic rarely exist. A new chaotic system, obtained by making the change on coordinate to the Hu chaotic system, can generate very complex attractors with four-wing topological structure and three positive Lyapunov exponents over a wide range of parameters. The influence of parameters varying to system dynamics is analyzed, computer simulations and bifurcation analysis is also verified in this paper.

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8

Boukabou, A., A. Chebbah, and A. Belmahboul. "Stabilizing Unstable Periodic Orbits of the Multi-Scroll Chua's Attractor." Nonlinear Analysis: Modelling and Control 12, no. 4 (October 25, 2007): 469–77. http://dx.doi.org/10.15388/na.2007.12.4.14678.

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This paper addresses the control of the n-scroll Chua’s circuit. It will be shown how chaotic systems with multiple unstable periodic orbits (UPOs) detected in the Poincar´e section can be stabilized as well as taking the system dynamics from one UPO to another.

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9

Bouallegue, Kais, Abdessattar Chaari, and Ahmed Toumi. "Multi-scroll and multi-wing chaotic attractor generated with Julia process fractal." Chaos, Solitons & Fractals 44, no. 1-3 (January 2011): 79–85. http://dx.doi.org/10.1016/j.chaos.2010.12.005.

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10

GÜNAY, ENİS. "A NEW AUTONOMOUS CHAOS GENERATOR FROM STATE CONTROLLED-CELLULAR NEURAL NETWORKS." International Journal of Bifurcation and Chaos 22, no. 03 (March 2012): 1250069. http://dx.doi.org/10.1142/s0218127412500691.

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In this study, a new autonomous chaos generator is presented via State Controlled-Cellular Neural Networks (SC-CNNs). From the numerical and circuit simulations, it has been shown that the proposed SC-CNN consisting of three cells can be easily used in chaotic applications as a chaos generator. After presenting the double scroll generation, the presented SC-CNN system is used either in multi-scroll chaotic attractor generation by adding a trigonometric function generator and or to construct a SC-CNN based chaotic masking system with feedback algorithm.

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11

Xiao-Hua, Luo, Tu Zheng-Wei, Liu Xi-Rui, Cai Chang, Liang Yi-Long, and Gong Pu. "Implementation of a novel two-attractor grid multi-scroll chaotic system." Chinese Physics B 19, no. 7 (July 2010): 070510. http://dx.doi.org/10.1088/1674-1056/19/7/070510.

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12

Wang, Ning, Bo-Cheng Bao, Quan Xu, Mo Chen, and Ping Ye Wu. "Emerging multi-double-scroll attractor from variable-boostable chaotic system excited by multi-level pulse." Journal of Engineering 2018, no. 1 (January 1, 2018): 42–44. http://dx.doi.org/10.1049/joe.2017.0403.

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13

Ji’e, Musha, Dengwei Yan, Lidan Wang, and Shukai Duan. "Hidden Attractor and Multistability in a Novel Memristor-Based System Without Symmetry." International Journal of Bifurcation and Chaos 31, no. 11 (September 2, 2021): 2150168. http://dx.doi.org/10.1142/s0218127421501686.

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Memristor, as a typical nonlinear element, is able to produce chaotic signals in chaotic systems easily. Chaotic systems have potential applications in secure communications, information encryption, and other fields. Therefore, it is of importance to generate abundant dynamic behaviors in a single chaotic system. In this paper, a novel memristor-based chaotic system without equilibrium points is proposed. One of the essential features is the absence of symmetry in this system, which increases the complexity of the new system. Then, the nonlinear dynamic behaviors of the system are analyzed in terms of chaos diagrams, bifurcation diagrams, Poincaré maps, Lyapunov exponent spectra, the sum of Lyapunov exponents, phase portraits, 0–1 test, recurrence analysis and instantaneous phase. The results of the sum of Lyapunov exponents show that the given system is a quasi-Hamiltonian system with certain initial conditions (IC) and parameters. Next, other critical phenomena, such as hidden multi-scroll attractors, abundant coexistence characteristics, are found characterized through basins of attraction and others. Especially, it reveals some rare phenomena in other systems that multiple hidden hyperchaotic attractors coexist. Finally, the circuit implementation based on Micro Control Unit (MCU) confirms theoretical analysis and the numerical simulation.

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14

Campos-Cantón, E. "Chaotic attractors based on unstable dissipative systems via third-order differential equation." International Journal of Modern Physics C 27, no. 01 (January 2016): 1650008. http://dx.doi.org/10.1142/s012918311650008x.

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In this paper, we present an approach how to yield 1D, 2D and 3D-grid multi-scroll chaotic systems in [Formula: see text] based on unstable dissipative systems via third-order differential equation. This class of systems is constructed by a switching control law(SCL) changing the equilibrium point of an unstable dissipative system. The switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor.

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15

Zhang, Xin, and Chunhua Wang. "A Novel Multi-Attractor Period Multi-Scroll Chaotic Integrated Circuit Based on CMOS Wide Adjustable CCCII." IEEE Access 7 (2019): 16336–50. http://dx.doi.org/10.1109/access.2019.2894853.

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16

Li, Dan, Wei Hua Chen, Yang Wang, and De Li Cui. "Research on Multi-Scroll Chaotic Attractors Synchronization Technique." Applied Mechanics and Materials 635-637 (September 2014): 1132–35. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.1132.

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Multi-scroll chaotic attractors synchronization technique is a research focuses in recent years. This paper focuses on multi-scroll chaotic attractors in the four-dimensional system. It uses variable feedback synchronous method to achieve the two 4-scroll chaotic attractors’ synchronization. The feasibility of this method is proved by theoretical analysis and numerical simulation. Simultaneously, it gets a better synchronization results.

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17

Tang, Zi Long, and Si Min Yu. "Multi-Scroll Chaotic System Based on Even-Symmetric Step-Wave Sequence Control." Applied Mechanics and Materials 340 (July 2013): 760–66. http://dx.doi.org/10.4028/www.scientific.net/amm.340.760.

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This paper presents a new approach for generating multi-scroll chaotic attractors. First, a new double scroll chaotic system with piecewise linearity and invariance under the transformationis introduced. Then, by using the even-symmetric step-wave sequence switching control method in this system to extend the number of saddle-focus points of index 2, the intended multi-scroll chaotic attractors can be obtained. A circuit for generating multi-scroll chaotic attractors is designed, and the experimental results are also given, confirming the consistency of the theory design and circuit implementation.

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18

Li, Dan, and Lu Wang. "A New Multi-Scroll Chaotic Attractors Synchronization Technique." Applied Mechanics and Materials 220-223 (November 2012): 1226–29. http://dx.doi.org/10.4028/www.scientific.net/amm.220-223.1226.

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Multi-scroll chaotic attractors synchronization technique is a research focuses in recent years. This paper focuses on multi-scroll chaotic attractors in the four-dimensional system. It uses variable feedback synchronous method and active-passive synchronous method to achieve the two 6-scroll chaotic attractors’ synchronization. The feasibility of this method is proved by theoretical analysis and numerical simulation. Simultaneously, it gets a better synchronization results.

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19

Luo, Xiao Wen, and Chun Hua Wang. "Generation and Circuit Implementation of Multi-Scroll Chaotic Attractors with Controllable Direction." Applied Mechanics and Materials 513-517 (February 2014): 4559–62. http://dx.doi.org/10.4028/www.scientific.net/amm.513-517.4559.

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An approach for generating multi-scroll chaotic attractors with controllable direction in one plane is proposed. Firstly, an appropriate nonlinear function is selected to control the number and direction of multi-scroll chaotic attractors in the three-order Jerk system. Then, we add new control function to Jerk system and observe Lyapunov exponent spectrum of relative coefficient and the change of equilibrium points. Different multi-scroll chaotic attractors with controllable direction are generated by adjusting the coefficient of the control function in a plane. The implementation of circuit verifies the feasibility of this method.

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20

WANG, FA-QIANG, and CHONG-XIN LIU. "GENERATION OF MULTI-SCROLL CHAOTIC ATTRACTORS VIA THE SAW-TOOTH FUNCTION." International Journal of Modern Physics B 22, no. 15 (June 20, 2008): 2399–405. http://dx.doi.org/10.1142/s0217979208039575.

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A new method for generating the multi-scroll chaotic attractors is introduced. It is demonstrated that the multi-scroll chaotic attractors can be generated using the saw-tooth function series and different number of scrolls can be designed easily by modifying the natural number n of the saw-tooth function. Various scroll attractors are illustrated not only by computer simulation, but also by the realization of an electronic circuit experiment on EWB.

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21

Zhang, Sen, Jiahao Zheng, Xiaoping Wang, Zhigang Zeng, and Xuenan Peng. "A Novel Nonideal Flux-Controlled Memristor Model for Generating Arbitrary Multi-Double-Scroll and Multi-Double-Wing Attractors." International Journal of Bifurcation and Chaos 31, no. 06 (May 2021): 2150086. http://dx.doi.org/10.1142/s0218127421500863.

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This paper proposes a novel nonideal flux-controlled memristor model with a multipiecewise linear memductance function, which can be used to construct a memristive multi-scroll or multi-wing chaotic system. Importantly, arbitrary multi-double-scroll and multi-double-wing attractors can be generated depending on this memristor model directly and without the need to change the original nonlinear terms of the system. Another highlight is that the odd or even number of the double-scroll and double-wing attractors can also be freely controlled by the memristor model. To further illustrate these unique features, by introducing the memristor model into two classical chaotic systems, i.e. Jerk system and Lorenz system, multi-double-scroll and multi-double-wing chaotic attractors are obtained respectively. The formation mechanism of the multi-double-wing and multi-double-scroll attractors is also discussed. Moreover, the randomness of the chaotic binary sequences generated by the proposed memristor model is tested by the National Institute of Standards and Technology test suite. The tested results are better than those of the well-known Lorenz system. Furthermore, the corresponding circuits are constructed. The experimental results and the numerical simulations coincide well with each other, showing the effectiveness and feasibility of the proposed memristor model.

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22

Carbajal-Gomez, Victor, Esteban Tlelo-Cuautle, Carlos Sanchez-Lopez, and Francisco Fernandez-Fernandez. "PVT-Robust CMOS Programmable Chaotic Oscillator: Synchronization of Two 7-Scroll Attractors." Electronics 7, no. 10 (October 16, 2018): 252. http://dx.doi.org/10.3390/electronics7100252.

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Designing chaotic oscillators using complementary metal-oxide-semiconductor (CMOS) integrated circuit technology for generating multi-scroll attractors has been a challenge. That way, we introduce a current-mode piecewise-linear (PWL) function based on CMOS cells that allow programmable generation of 2–7-scroll chaotic attractors. The mathematical model of the chaotic oscillator designed herein has four coefficients and a PWL function, which can be varied to provide a high value of the maximum Lyapunov exponent. The coefficients are implemented electronically by designing operational transconductance amplifiers that allow programmability of their transconductances. Design simulations of the chaotic oscillator are provided for the 0.35 μ m CMOS technology. Post-layout and process–voltage–temperature (PVT) variation simulations demonstrate robustness of the multi-scroll chaotic attractors. Finally, we highlight the synchronization of two seven-scroll attractors in a master–slave topology by generalized Hamiltonian forms and observer approach. Simulation results show that the synchronized CMOS chaotic oscillators are robust to PVT variations and are suitable for chaotic secure communication applications.

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23

Gotthans, Tomáš, and Zdeněk Hruboš. "Multi Grid Chaotic Attractors with Discrete Jumps." Journal of Electrical Engineering 64, no. 2 (March 1, 2013): 118–22. http://dx.doi.org/10.2478/jee-2013-0017.

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In this paper the discrete step functions are used in order to generate m×n scroll chaotic hypercube attractors. The design and realization of multi-scroll attractors depends on synthesizing the nonlinearity with an electrical circuit. The essence of the novel approach is in designing the transfer function with analog to digital converters connected directly without any microcomputer, instead of using standard comparator or hysteresis methods. Therefore there is no special need for synthesizing the nonlinearity towards m × n scroll chaotic attractors. The approach is verified with PSpice 16.0 circuit simulator and experimentally measured.

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24

Li, Dan, Meng Jin, Zhen Fan, and Xian Da Dong. "Achieving the Multi-Scroll Chaotic Attractors’ Synchronization in the Four-Dimensional System by Driving-Response Synchronization Method." Applied Mechanics and Materials 635-637 (September 2014): 1076–80. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.1076.

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Multi-scroll chaotic attractors’ synchronization technology is one of the important research achievements in recent years.This paper uses driving-response synchronization method to achieve the two 6-scroll chaotic attractors’ synchronization in the four-dimensional syetem.The feasibility of this method is proved by theoretical analysis and numerical simulation.

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25

Lü, Jinhu, K. Murali, Sudeshna Sinha, Henry Leung, and M. A. Aziz-Alaoui. "Generating multi-scroll chaotic attractors by thresholding." Physics Letters A 372, no. 18 (April 2008): 3234–39. http://dx.doi.org/10.1016/j.physleta.2008.01.065.

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26

Zhang, Chao Xia. "Generation and Circuit Implementation of Grid Multi-Scroll Chaotic Attractors." Applied Mechanics and Materials 336-338 (July 2013): 1554–57. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.1554.

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In this paper, grid multi-scroll chaotic attractors are firstly generated. The maximum Lyapunov exponent is further calculated to prove the existence of chaos in designed system. An improved module-based circuit is designed for realizing 5×3 grid scroll chaotic attractors, and the experimental results are also obtained, which is consistent with the numerical simulations.

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27

SRINIVASAN, K., I. RAJA MOHAMED, K. MURALI, M. LAKSHMANAN, and SUDESHNA SINHA. "DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER." International Journal of Bifurcation and Chaos 21, no. 03 (March 2011): 725–35. http://dx.doi.org/10.1142/s0218127411028751.

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A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

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28

Türk, Mustafa, and Fikret Ata. "The multi‐mode chaotic behaviors:N+Nand 2DN‐scroll chaotic attractors." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 25, no. 4 (October 2006): 929–39. http://dx.doi.org/10.1108/03321640610684088.

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29

Han, Fengling, Jiankun Hu, Xinghuo Yu, and Yi Wang. "Fingerprint images encryption via multi-scroll chaotic attractors." Applied Mathematics and Computation 185, no. 2 (February 2007): 931–39. http://dx.doi.org/10.1016/j.amc.2006.07.030.

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30

ZHANG, CHAO-XIA, SI-MIN YU, and YUN ZHANG. "DESIGN AND REALIZATION OF MULTI-WING CHAOTIC ATTRACTORS VIA SWITCHING CONTROL." International Journal of Modern Physics B 25, no. 16 (June 30, 2011): 2183–94. http://dx.doi.org/10.1142/s021797921110059x.

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In this paper, a novel approach for generating multi-wing chaotic attractors via switching control is proposed. By using a switching controller, multi-wing chaotic attractors can be generated from a double-wing system. The presented method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. Furthermore, the basic dynamical behaviors, including equilibrium points, maximum Lyapunov exponents and bifurcations, are further investigated. An improved module-based unified circuit is designed for realizing 4, 6, 8 and 10-wing chaotic attractors, and the experimental result is also demonstrated, which is consistent with the numerical simulation.

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31

Ding, Pengfei, and Xiaoyi Feng. "Generation of Multi-Scroll Chaotic Attractors from a Jerk Circuit with a Special Form of a Sine Function." Electronics 9, no. 5 (May 19, 2020): 842. http://dx.doi.org/10.3390/electronics9050842.

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A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are infinite equilibrium points in this system, the scroll number of the generated chaotic attractors is certain under appropriate system parameters. The dynamical properties of the proposed chaotic system are studied through Lyapunov exponents, phase portraits, and bifurcation diagrams. It is found that the scroll number of the chaotic system in the left and right part of the x-y plane can be determined arbitrarily by adjusting the values of the parameters in the SFSF, and the size of attractors is dominated by the frequency of the SFSF. Finally, an electronic circuit of the proposed chaotic system is implemented on Pspice, and the simulation results of electronic circuit are in agreement with the numerical ones.

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32

Ding, Pengfei, Xiaoyi Feng, and Lin Fa. "Generation of 3-D Grid Multi-Scroll Chaotic Attractors Based on Sign Function and Sine Function." Electronics 9, no. 12 (December 15, 2020): 2145. http://dx.doi.org/10.3390/electronics9122145.

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A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a modified sine function (MSF). In addition, the scrolls in Y and Z directions are generated by the sign function series, which are the superposition of some sign functions with different time-shift values. In the X-direction, the scroll number is adjusted by changing the comparative voltages of the MSF, and the ones in Y and Z directions are regulated by the sign function. The basic dynamics of Lyapunov exponent spectrum, phase diagrams, bifurcation diagram and equilibrium points distribution were studied. Furthermore, the circuits of the chaotic system are designed by Multisim10, and the circuit simulation results indicate the feasibility of the proposed chaotic system for generating chaotic attractors. On the basis of the circuit simulations, the hardware circuits of the system are designed for experimental verification. The experimental results match with the circuit simulation results, this powerfully proves the correctness and feasibility of the proposed system for generating 3-D grid multi-scroll chaotic attractors.

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33

WANG, CHUN HUA, HAO XU, and FEI YU. "A NOVEL APPROACH FOR CONSTRUCTING HIGH-ORDER CHUA'S CIRCUIT WITH MULTI-DIRECTIONAL MULTI-SCROLL CHAOTIC ATTRACTORS." International Journal of Bifurcation and Chaos 23, no. 02 (February 2013): 1350022. http://dx.doi.org/10.1142/s0218127413500223.

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A novel approach for constructing a high-order Chua's circuit is proposed. Based on a dual-port RCL network, a high-order Chua's circuit which can generate multi-directional multi-scroll (MDMS) chaotic attractors can be realized by introducing a RC structure and suitable nonlinear functions. First, a fourth-order Chua's circuit is achieved by adding a capacitor, a resistance and a controlled-source constituted by stair functions in the third-order Chua's circuit. And then, this recursive method can be adopted in higher-order Chua's circuit which can generate multi-scroll chaotic attractors in more directions. Finally, a sixth-order Chua's circuit is designed and its experimental results demonstrate the feasibility of this method.

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34

Sun, Guanghui, Mao Wang, Lilian Huang, and Liqun Shen. "Generating Multi-Scroll Chaotic Attractors via Switched Fractional Systems." Circuits, Systems, and Signal Processing 30, no. 6 (February 1, 2011): 1183–95. http://dx.doi.org/10.1007/s00034-011-9272-2.

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35

Liu, Song, Yaping Wei, Jingyi Liu, Shiqiang Chen, and Guoping Zhang. "Multi-Scroll Chaotic System Model and Its Cryptographic Application." International Journal of Bifurcation and Chaos 30, no. 13 (October 2020): 2050186. http://dx.doi.org/10.1142/s0218127420501862.

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This paper introduces a new chaotic system model that could generate multi-direction multi-scroll (MDMS) chaotic attractors. The fundamental dynamics characteristics of this model are investigated, and the feasibility of the proposed method is confirmed by numerical simulation based on MATLAB. Additionally, the new chaotic system is implemented in FPGA-based platform. Implementation results are the same in MATLAB and FPGA, which indicates that they are suitable for practical applications. To investigate the cryptographic application of the new chaotic system, the chaotic sequences generated by the proposed system are used to encrypt images. The key space of the algorithm as well as key sensitivity, plain image sensitivity, plaintext histogram, correlation and information entropy are simulated and analyzed. In contrast to several encryption schemes, the proposed algorithm is very sensitive to plaintext and the key.

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36

Jia, Mei-Mei, Hao-Gang Jiang, and Wen-Jing Li. "Generation and application of novel Chua multi-scroll chaotic attractors." Acta Physica Sinica 68, no. 13 (2019): 130503. http://dx.doi.org/10.7498/aps.68.20182183.

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37

Muñoz-Pacheco, J. M., E. Tlelo-Cuautle, I. Toxqui-Toxqui, C. Sánchez-López, and R. Trejo-Guerra. "Frequency limitations in generating multi-scroll chaotic attractors using CFOAs." International Journal of Electronics 101, no. 11 (January 30, 2014): 1559–69. http://dx.doi.org/10.1080/00207217.2014.880999.

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38

Wang Fa-Qiang, Liu Chong-Xin, and Lu Jun-Jie. "Emulation of multi-scroll chaotic attractors in four-dimensional systems." Acta Physica Sinica 55, no. 7 (2006): 3289. http://dx.doi.org/10.7498/aps.55.3289.

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39

Yan, Minxiu, and Hui Xu. "The multi-scroll hyper-chaotic coexistence attractors and its application." Signal Processing: Image Communication 95 (July 2021): 116210. http://dx.doi.org/10.1016/j.image.2021.116210.

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Luo, Xiaowen, Chunhua Wang, and Zhao Wan. "Grid multi-wing butterfly chaotic attractors generated from a new 3-D quadratic autonomous system." Nonlinear Analysis: Modelling and Control 19, no. 2 (April 10, 2014): 272–85. http://dx.doi.org/10.15388/na.2014.2.9.

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Abstract:

Due to the dynamic characteristics of the Lorenz system, multi-wing chaotic systems are still confined in the positive half-space and fail to break the threshold limit. In this paper, a new approach for generating complex grid multi-wing attractors that can break the threshold limit via a novel nonlinear modulating function is proposed from the firstly proposed double-wing chaotic system. The proposed method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. The new system is autonomous and can generate various grid multi-wing butterfly chaotic attractors without requiring any external forcing, it also can produce grid multi-wing both on the xz-plane and yz-plane. Basic properties of the new system such as dissipation property, equilibrium, stability, the Lyapunov exponent spectrum and bifurcation diagram are introduced by numerical simulation, theoretical analysis and circuit experiment, which confirm that the multi-wing attractors chaotic system has more rich and complicated chaotic dynamics. Finally, a novel module-based unified circuit is designed which provides some principles and guidelines for future circuitry design and engineering application. The circuit experimental results are consistent with the numerical simulation results.

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41

Günay, Enis, and Kenan Altun. "Multi-Scroll Chaotic Attractors in SC-CNN via Hyperbolic Tangent Function." Electronics 7, no. 5 (May 9, 2018): 67. http://dx.doi.org/10.3390/electronics7050067.

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Luo Xiao-Hua, Li Hua-Qing, and Dai Xiang-Guang. "A family of multi-scroll chaotic attractors and its circuit design." Acta Physica Sinica 57, no. 12 (2008): 7511. http://dx.doi.org/10.7498/aps.57.7511.

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Chen, Liping, Wei Pan, Ranchao Wu, J. A. Tenreiro Machado, and António M. Lopes. "Design and implementation of grid multi-scroll fractional-order chaotic attractors." Chaos: An Interdisciplinary Journal of Nonlinear Science 26, no. 8 (August 2016): 084303. http://dx.doi.org/10.1063/1.4958717.

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Deng, Weihua, and Jinhu Lü. "Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system." Physics Letters A 369, no. 5-6 (October 2007): 438–43. http://dx.doi.org/10.1016/j.physleta.2007.04.112.

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Wang, Chunhua, Xiaowen Luo, and Zhao Wan. "Generation and circuit implementation of multi-block multidirectional grid multi-scroll chaotic attractors." Optik 125, no. 22 (November 2014): 6716–21. http://dx.doi.org/10.1016/j.ijleo.2014.07.084.

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Wang Fa-Qiang and Liu Chong-Xin. "Simulation of a family of multi-folded torus and multi-scroll chaotic attractors." Acta Physica Sinica 56, no. 4 (2007): 1983. http://dx.doi.org/10.7498/aps.56.1983.

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Lu, Haikong, Karthikeyan Rajagopal, Fahimeh Nazarimehr, and Sajad Jafari. "A New Multi-Scroll Megastable Oscillator Based on the Sign Function." International Journal of Bifurcation and Chaos 31, no. 08 (June 26, 2021): 2150140. http://dx.doi.org/10.1142/s0218127421501406.

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Abstract:

A chaotic system that can show multiscroll and megastable attractors is studied in this paper. Two cases of the system with periodic and quasi-periodic excitations are discussed. Various stabilities of the system determined by changing parameters and initial values are investigated for both cases. In Case-A of the proposed system, multiscroll attractors are shown for the various parameter values. In Case-B with quasi-periodic excitation, the system shows various multiscroll attractors. Dynamical properties of these two cases are studied using the bifurcation diagram and Lyapunov exponents.

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XU, FEI, PEI YU, and XIAOXIN LIAO. "SYNCHRONIZATION AND STABILIZATION OF MULTI-SCROLL INTEGER AND FRACTIONAL ORDER CHAOTIC ATTRACTORS GENERATED USING TRIGONOMETRIC FUNCTIONS." International Journal of Bifurcation and Chaos 23, no. 08 (August 2013): 1350145. http://dx.doi.org/10.1142/s0218127413501459.

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Sigmoidal functions are usually used to characterize the behavior of dynamical systems, in particular, for neural networks. Recently, multilevel piecewise linear functions have been employed in cellular neural networks (CNN). In this paper, we first use the inverse trigonometric function, tan -1(x), to generate a series of trigonometric functions to obtain one-, two- and three-directional multi-scroll integer and fractional order chaotic attractors. Then, based upon the properties of the chaotic systems, simple feedback control laws are designed to stabilize or synchronize the integer and fractional order chaotic systems. Numerical simulations are presented to demonstrate the applicability of theoretical predictions.

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Wang, Chunhua, Xiaoming Liu, and Hu Xia. "Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system." Chaos: An Interdisciplinary Journal of Nonlinear Science 27, no. 3 (March 2017): 033114. http://dx.doi.org/10.1063/1.4979039.

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Zhang, Chaoxia, and Simin Yu. "Generation of grid multi-scroll chaotic attractors via switching piecewise linear controller." Physics Letters A 374, no. 30 (July 2010): 3029–37. http://dx.doi.org/10.1016/j.physleta.2010.05.043.

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