Готові списки джерел за темами / Piecewise-smooth dynamics

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Добірка наукової літератури з теми "Piecewise-smooth dynamics"

Автор: Grafiati
Опубліковано: 11 березня 2023

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Статті в журналах з теми "Piecewise-smooth dynamics"

1

ZHUSUBALIYEV, ZHANYBAI T., EVGENIY A. SOUKHOTERIN, and ERIK MOSEKILDE. "BORDER-COLLISION BIFURCATIONS AND CHAOTIC OSCILLATIONS IN A PIECEWISE-SMOOTH DYNAMICAL SYSTEM." International Journal of Bifurcation and Chaos 11, no. 12 (December 2001): 2977–3001. http://dx.doi.org/10.1142/s0218127401003991.

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Анотація:
Many problems of engineering and applied science result in the consideration of piecewise-smooth dynamical systems. Examples are relay and pulse-width control systems, impact oscillators, power converters, and various electronic circuits with piecewise-smooth characteristics. The subject of investigation in the present paper is the dynamical model of a constant voltage converter which represents a three-dimensional piecewise-smooth system of nonautonomous differential equations. A specific type of phenomena that arise in the dynamics of piecewise-smooth systems are the so-called border-collision bifurcations. The paper contains a detailed analysis of this type of bifurcational transition in the dynamics of the voltage converter, in particular, the merging and subsequent disappearance of cycles of different types, change of solution type, and period-doubling, -tripling, -quadrupling and -quintupling. We show that a denumerable set of unstable cycles can arise together with stable cycles at border-collision bifurcations. The characteristic peculiarities of border-collision bifurcational transitions in piecewise-smooth systems are described and we provide a comparison with some recent results.
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2

Li, Shuangbao, Wei Zhang, and Yuxin Hao. "Melnikov-Type Method for a Class of Discontinuous Planar Systems and Applications." International Journal of Bifurcation and Chaos 24, no. 02 (February 2014): 1450022. http://dx.doi.org/10.1142/s0218127414500229.

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In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed piecewise smooth planar system. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise smooth homoclinic solution transversally crossing the switching manifold. The Melnikov-type function is explicitly derived by using the Hamiltonian function to measure the distance of the perturbed stable and unstable manifolds. Finally, we apply the obtained results to study the chaotic dynamics of a concrete piecewise smooth system.
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3

Kumar, Aloke, Soumitro Banerjee, and Daniel P. Lathrop. "Dynamics of a piecewise smooth map with singularity." Physics Letters A 337, no. 1-2 (March 2005): 87–92. http://dx.doi.org/10.1016/j.physleta.2005.01.046.

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4

Novaes, Douglas D., and Mike R. Jeffrey. "Regularization of hidden dynamics in piecewise smooth flows." Journal of Differential Equations 259, no. 9 (November 2015): 4615–33. http://dx.doi.org/10.1016/j.jde.2015.06.005.

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5

de Simoi, Jacopo, and Dmitry Dolgopyat. "Dynamics of some piecewise smooth Fermi-Ulam models." Chaos: An Interdisciplinary Journal of Nonlinear Science 22, no. 2 (June 2012): 026124. http://dx.doi.org/10.1063/1.3695379.

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6

Li, Shuangbao, Wensai Ma, Wei Zhang, and Yuxin Hao. "Melnikov Method for a Class of Planar Hybrid Piecewise-Smooth Systems." International Journal of Bifurcation and Chaos 26, no. 02 (February 2016): 1650030. http://dx.doi.org/10.1142/s0218127416500309.

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Анотація:
In this paper, we extend the well-known Melnikov method for smooth systems to a class of periodic perturbed planar hybrid piecewise-smooth systems. In this class, the switching manifold is a straight line which divides the plane into two zones, and the dynamics in each zone is governed by a smooth system. When a trajectory reaches the separation line, then a reset map is applied instantaneously before entering the trajectory in the other zone. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise-smooth homoclinic solution transversally crossing the switching manifold. Then, we study the persistence of the homoclinic orbit under a nonautonomous periodic perturbation and the reset map. To achieve this objective, we obtain the Melnikov function to measure the distance of the perturbed stable and unstable manifolds and present the theorem for homoclinic bifurcations for the class of planar hybrid piecewise-smooth systems. Furthermore, we employ the obtained Melnikov function to detect the chaotic boundaries for a concrete planar hybrid piecewise-smooth system.
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7

Langer, Cameron K., and Bruce N. Miller. "Regular and chaotic dynamics of a piecewise smooth bouncer." Chaos: An Interdisciplinary Journal of Nonlinear Science 25, no. 7 (July 2015): 073114. http://dx.doi.org/10.1063/1.4923747.

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Roy, Indrava, Mahashweta Patra, and Soumitro Banerjee. "Shilnikov-type dynamics in three-dimensional piecewise smooth maps." Chaos, Solitons & Fractals 133 (April 2020): 109655. http://dx.doi.org/10.1016/j.chaos.2020.109655.

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9

Li, Denghui, Hebai Chen, and Jianhua Xie. "Smale Horseshoe in a Piecewise Smooth Map." International Journal of Bifurcation and Chaos 29, no. 04 (April 2019): 1950051. http://dx.doi.org/10.1142/s0218127419500512.

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Анотація:
We investigate the chaotic dynamics of a two-dimensional piecewise smooth map. The map represents the normal form of a discrete time representation of impact oscillators near grazing states. It is proved that, in certain region of the parameter space, the nonwandering set of the map is contained in a bounded region and that, restricted to the nonwandering set, the map is topologically conjugate to the two-sided shift map on two symbols.
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10

DONDE, VAIBHAV, and IAN A. HISKENS. "SHOOTING METHODS FOR LOCATING GRAZING PHENOMENA IN HYBRID SYSTEMS." International Journal of Bifurcation and Chaos 16, no. 03 (March 2006): 671–92. http://dx.doi.org/10.1142/s0218127406015040.

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Анотація:
Hybrid systems are typified by strong coupling between continuous dynamics and discrete events. For such piecewise smooth systems, event triggering generally has a significant influence over subsequent system behavior. Therefore, it is important to identify situations where a small change in parameter values alters the event triggering pattern. The bounding case, which separates regions of (generally) quite different dynamic behaviors, is referred to as grazing. At a grazing point, the system trajectory makes tangential contact with an event triggering hypersurface. The paper formulates conditions governing grazing points. Both transient and periodic behaviors are considered. The resulting boundary value problems are solved using shooting methods that are applicable for general nonlinear hybrid (piecewise smooth) dynamical systems. The grazing point formulation underlies the development of a continuation process for exploring parametric dependence. It also provides the basis for an optimization technique that finds the smallest parameter change necessary to induce grazing. Examples are drawn from power electronics, power systems and robotics, all of which involve intrinsic interactions between continuous dynamics and discrete events.
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Більше джерел

Дисертації з теми "Piecewise-smooth dynamics"

1

Geffert, Paul Matthias. "Nonequilibrium dynamics of piecewise-smooth stochastic systems." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/46783.

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Piecewise-smooth stochastic systems have attracted a lot of interest in the last decades in engineering science and mathematics. Many investigations have focused only on one-dimensional problems. This thesis deals with simple two-dimensional piecewise-smooth stochastic systems in the absence of detailed balance. We investigate the simplest example of such a system, which is a pure dry friction model subjected to coloured Gaussian noise. The nite correlation time of the noise establishes an additional dimension in the phase space and gives rise to a non-vanishing probability current. Our investigation focuses on stick-slip transitions, which can be related to a critical value of the noise correlation time. Analytical insight is provided by applying the uni ed coloured noise approximation. Afterwards, we extend our previous model by adding viscous friction and a constant force. Then we perform a similar analysis as for the pure dry friction case. With parameter values close to the deterministic stick-slip transition, we observe a non-monotonic behaviour of the probability of sticking by increasing the correlation time of the noise. As the eigenvalue spectrum is not accessible for the systems with coloured noise, we consider the eigenvalue problem of a dry friction model with displacement, velocity and Gaussian white noise. By imposing periodic boundary conditions on the displacement and using a Fourier ansatz, we can derive an eigenvalue equation, which has a similar form in comparison to the known one-dimensional problem for the velocity only. The eigenvalue analysis is done for the case without a constant force and with a constant force separately. Finally, we conclude our ndings and provide an outlook on related open problems.
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2

Homer, Martin Edward. "Bifurcations and dynamics of piecewise smooth dynamical systems of arbitrary dimension." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299271.

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3

Moreno, Font Vanessa. "Unfolding piecewise-smooth dynamics in a single inductor multiple-output switching converter." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/6593.

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Els convertidors commutats de potència són solucions apropiades per subministrar energia a dispositius electrònics per la seva elevada eficiència i reduït cost. El seu ús extensiu en les últimes dècades ha motivat els investigadors a millorar els seus dissenys i aprofundir en la comprensió del seu comportament el qual, com la majoria de dispositius electrònics de potència, presenta dinàmiques no lineals. Recentment, han aparegut equipaments electrònics que disposen de múltiples càrregues com són els PDA, telèfons mòbils, MP3... Freqüentment, aquestes aplicacions necessiten múltiples alimentacions amb doble polaritat. Els convertidors amb inductor únic i múltiples sortides, Single-Inductor Multiple-Input Multiple-Output (SIMIMO), han esdevingut solucions per subministrar energia a dispositius de baixa potència, com pantalles LCD, i per carregar bateries ja que l'ús d'un sol inductor redueix significativament la mida del convertidor.
La inherent naturalesa commutada d'aquests sistemes classifica la seva dinàmica dins el camp de sistemes d'estructura variable, Variable Structure Systems (VSS), els quals també es coneixen com a sistemes suaus a trams, Piecewise Smooth (PWS) systems. Atès que la teoria clàssica per a sistemes suaus no pot explicar completament el seu comportament, en els últims anys s'han dirigit molts esforços cap a la recerca de les propietats de la dinàmica no suau en diferent camps d'aplicació.
Aquesta tesi aprofundeix en la caracterització de convertidors SIMIMO, que ens permetrà provar la seva viabilitat. Es proposen dues estratègies de control basades en el conegut control PWM (Pulse Width Modulation). En la primera alternativa, el control ens permet regular un convertidor amb dues entrades i dues sortides (Two-Input Two-Output , SITITO), amb polaritats oposades. En aquest cas, les dues senyals moduladores necessàries són generades sincronitzadament i per aquest motiu, en aquesta tesi ens referirem a aquesta estratègia de control PWM com a SPC (Single Phase Control) en contraposició amb la segona alternativa, la qual serà anomenada IC (Interleaved Control), capaç de regular un número generalitzat de sortides. Aquest control està basat en l'ús de diverses senyals moduladores, tantes com a sortides, les quals s'han desfasat progressivament.
La dinàmica dels convertidors SIMIMO, al igual que els convertidors bàsics contínua - contínua, exhibeix una rica varietat de fenòmens, els quals engloben des de bifurcacions suaus, com són les bifurcacions de doblament de període (period doubling bifurcation), Saddle-Node o Hopf, fins a bifurcacions no suaus. Un cop verificada l'existència de dinàmica estable quan els paràmetres s'han seleccionatapropiadament, aquesta tesi aborda la recerca de models amb els quals analitzar la complexa dinàmica dels convertidors en un rang ampli de paràmetres. Es proposen i analitzen alguns models que s'utilitzen complementàriament: els anomenats averaged models, amb els quals es pot analitzar la dinàmica lenta, i els models discrets, capaços de detectar les inestabilitats degudes a la dinàmica ràpida. A més a més, alguns d'aquest models seran definits i analitzats. La seva utilitat s'ha provat no només en la predicció de la estabilitat, sinó també en la caracterització de bifurcacions no suaus presents en el circuit. Es demostra que senzills sistemes lineals a trams de dimensió ú proporcionen expressions analítiques per a les condicions d'estabilitat y existència de punts fixos. Per finalitzar, es desenvolupen mapes de dimensió més elevada per tal d'incrementar la precisió de les prediccions obtingudes mitjançat els averaged models i els models discrets.
L'anàlisi discreta del convertidor SITITO governat per cadascuna d'aquestes estratègies ha revelat que la dinàmica por ser modelada per un sistema lineal a trams en un rang específic de paràmetres. Fins on sabem, la bibliografia proporcionada sobre mapes PWL inclou tant mapes continus com discontinus, encara que limitats a dos trams. Per tant, aquesta tesi contribueix en el camp de la dinàmica no suau amb el desenvolupament de les propietats d'un mapa de tres trams.
Respecte al control IC, s'ha obtingut una anàlisi general de la seva estabilitat per a un convertidor SIMIMO amb un nombre genèric de càrregues. L'estudi de l'estabilitat del model discret de dimensió ú ha revelat l'existència d'un tipus de bifurcació no suau la qual ha estat classificada con una non-smooth pitchfork atesa l'aparició de nous punts fixos després de produir-se la bifurcació. Una anàlisi més detallada de models discrets de dimensions més elevades, associa aquesta bifurcació a una Neimark-Sacker.
Finalment, aquesta tesi també inclou alguns resultats experimentals obtinguts amb un prototip d'un convertidor SITITO, per tal de validar els escenaris trobats en l'anàlisi del comportament dinàmic del convertidor regulat per les dues estratègies de control.
Switching power converters are known to be appropriate solutions to supply energy to electronic devices owing to their high efficiency and low cost. Their extensive use in the last decades has motivated researches to improve their designs and to go deeply into the comprehension of their behavior which, like most power electronic devices, exhibit nonlinear dynamics. More recently, electronic equipments containing multiple loads have been arisen such as PDA, mobile phones, MP3... These applications frequently require multiple supplies with different polarities. Single-Inductor Multiple-Input Multiple-Output (SIMIMO) switching dc-dc converters are becoming as solutions to supply low power devices as LCD displays and to charge batteries due to the significant reduction of size because the use of a single inductor.
The inherent switching nature of these systems classifies their dynamics into the field of Variable Structure Systems (VSS), which are also known as Piecewise Smooth (PWS) systems. Due to the fact that their dynamics cannot be completely explained with the classical smooth theory, in the last years a lot of effort has been addressed towards the research on a theory of non-smooth dynamics motivated by different fields of application.
This dissertation deals with the dynamical characterization of SIMIMO converters, which can help us to prove their viability. Two strategies of control, both of them based on the widely used Pulse Width Modulation (PWM) control, are discussed. In the first alternative, the control is used to regulate a Two-Input Two-Output (SITITO) converter with opposite polarity. The two required modulate signals are generated synchronizely. This strategy of PWM control is called in this work Single Phase Control (SPC) in contrast to a second strategy, which is noted here as Interleaved Control (IC), capable of driving a generalized single inductor multiple-input multiple-output converters. This control is based on the use of various modulating signals, equal to the number of outputs, which are progressively time delayed.
The dynamics of the SIMIMO converters, just like of the basic dc-dc converters, presents a rich variety of nonlinear phenomena, which covers from smooth bifurcations, such as period doubling, Saddle-Node or Hopf bifurcations, to non-smooth bifurcations. After proving the existence of stable dynamics if appropriate parameters are selected, this dissertation will deal with the investigation of models to analyze the complex dynamics of the converter in a wide range of parameters. Several models are proposed and analyzed in this work. Averaged models, from which slow scale instability condition can be determined, and discrete-time models, able to prove fast scale instabilities, are used in a complementary way. Besides this, several approaches of these models will be established and validated. Their usefulness will be proved not only in the prediction of the stability, but also in the characterization of the non-smooth bifurcations presents in this converter. It will be shown that simple one-dimensional Piecewise-Linear (PWL) models provide analytical expressions for the stability and existence conditions of fixed points of the discrete-time models. Furthermore, higher dimensional maps are developed to improve the accuracy of the predictions obtained by means of one-dimensional maps and averaged models.
The discrete-time analysis of a SITITO converter driven by each of the two strategies of control has revealed that its dynamics can be modeled by a PWL with three trams in a specific range of parameters. To our best knowledge, the literature on PWL maps includes continuous and discontinuous maps but is limited to two trams. Therefore, this dissertation is a contribution in the field of non-smooth dynamics in base to the unfolding of specific dynamics of three-piece maps.
Concerning the IC control, a generalized analysis of the stability is obtained for a SIMIMO converter with a generic number of loads. The stability analysis of the one-dimensional model has revealed the existence of a type of non-smooth bifurcation, which has been classified in this dissertation as a non-smooth pitchfork owing to the appearance of two new fixed points after undergoing the bifurcation. Detailed analysis in higher dimensional maps associates this bifurcation to a Neimark-Sacker, whose existence cannot be predicted by averaged models.
This dissertation also includes some experimental results obtained with a SITITO dc-dc converter prototype, to validate some of the scenarios found in the analysis.
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4

Zhang, Yiwei. "Applications of transfer operator methods to the dynamics of low-dimensional piecewise smooth maps." Thesis, University of Exeter, 2012. http://hdl.handle.net/10036/3760.

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This thesis primarily concentrates on stochastic and spectral properties of the transfer operator generated by piecewise expanding maps (PWEs) and piecewise isometries (PWIs). We also consider the applications of the transfer operator in thermodynamic formalism. The original motivation stems from studies of one-dimensional PWEs. In particular, any one dimensional mixing PWE admits a unique absolutely continuous invariant probability measure (ACIP) and this ACIP has a bounded variation density. The methodology used to prove the existence of this ACIP is based on a so-called functional analytic approach and a key step in this approach is to show that the corresponding transfer operator has a spectral gap. Moreover, when a PWE has Markov property this ACIP can also be viewed as a Gibbs measure in thermodynamic formalism. In this thesis, we extend the studies on one-dimensional PWEs in several aspects. First, we use the functional analytic approach to study piecewise area preserving maps (PAPs) in particular to search for the ACIPs with multidimensional bounded variation densities. We also explore the relationship between the uniqueness of ACIPs with bounded variation densities and topological transitivity/ minimality for PWIs. Second, we consider the mixing and corresponding mixing rate properties of a collection of piecewise linear Markov maps generated by composing x to mx mod 1 with permutations in SN. We show that typical permutations preserve the mixing property under the composition. Moreover, by applying the Fredholm determinant approach, we calculate the mixing rate via spectral gaps and obtain the max/min spectral gaps when m,N are fixed. The spectral gaps can be made arbitrarily small when the permutations are fully refined. Finally, we consider the computations of fractal dimensions for generalized Moran constructions, where different iteration function systems are applied on different levels. By using the techniques in thermodynamic formalism, we approximate the fractal dimensions via the zeros of the Bowen's equation on the pressure functions truncated at each level.
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5

Svahn, Fredrik. "On the stability and control of piecewise-smooth dynamical systems with impacts and friction." Doctoral thesis, Stockholm : Skolan för teknikvetenskap, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11079.

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6

Rossi, Marco. "Dynamics and stability of discrete and continuous structures: flutter instability in piecewise-smooth mechanical systems and cloaking for wave propagation in Kirchhoff plates." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/322240.

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Анотація:
The first part of this Thesis deals with the analysis of piecewise-smooth mechanical systems and the definition of special stability criteria in presence of non-conservative follower forces. To illustrate the peculiar stability properties of this kind of dynamical system, a reference 2 d.o.f. structure has been considered, composed of a rigid bar, with one and constrained to slide, without friction, along a curved profile, whereas the other and is subject to a follower force. In particular, the curved constraint is assumed to be composed of two circular profiles, with different and opposite curvatures, defining two separated subsystems. Due to this jump in the curvature, located at the junction point between the curved profiles, the entire mechanical structure can be modelled by discontinuous equations of motion, the differential equations valid in each subsystem can be combined, leading to the definition of a piecewise-smooth dynamical system. When a follower force acts on the structure, an unexpected and counterintuitive behaviour may occur: although the two subsystems are stable when analysed separately, the composed structure is unstable and exhibits flutter-like exponentially-growing oscillations. This special form of instability, previously known only from a mathematical point of view, has been analysed in depth from an engineering perspective, thus finding a mechanical interpretation based on the concept of non-conservative follower load. Moreover, the goal of this work is also the definition of some stability criteria that may help the design of these mechanical piecewise-smooth systems, since classical theorems cannot be used for the investigation of equilibrium configurations located at the discontinuity. In the literature, this unusual behaviour has been explained, from a mathematical perspective, through the existence of a discontinuous invariant cone in the phase space. For this reason, starting from the mechanical system described above, the existence of invariant cones in 2 d.o.f. mechanical systems is investigated through Poincaré maps. A complete theoretical analysis on piecewise-smooth dynamical systems is presented and special mathematical properties have been discovered, valid for generic 2~d.o.f. piecewise-smooth mechanical systems, which are useful for the characterisation of the stability of the equilibrium configurations. Numerical tools are implemented for the analysis of a 2~d.o.f. piecewise-smooth mechanical system, valid for piecewise-linear cases and extendible to the nonlinear ones. A numerical code has been developed, with the aim of predicting the stability of a piecewise-linear dynamical system a priori, varying the mechanical parameters. Moreover, “design maps” are produced for a given subset of the parameters space, so that a system with a desired stable or unstable behaviour can easily be designed. The aforementioned results can find applications in soft actuation or energy harvesting. In particular, in systems devoted to exploiting the flutter-like instability, the range of design parameters can be extended by using piecewise-smooth instead of smooth structures, since unstable flutter-like behaviour is possible also when each subsystem is actually stable. The second part of this Thesis deals with the numerical analysis of an elastic cloak for transient flexural waves in Kirchhoff-Love plates and the design of special metamaterials for this goal. In the literature, relevant applications of transformation elastodynamics have revealed that flexural waves in thin elastic plates can be diverted and channelled, with the aim of shielding a given region of the ambient space. However, the theoretical transformations which define the elastic properties of this “invisibility cloak” lead to the presence of a strong compressive prestress, which may be unfeasible for real applications. Moreover, this theoretical cloak must present, at the same time, high bending stiffness and a null twisting rigidity. In this Thesis, an orthotropic meta-structural plate is proposed as an approximated elastic cloak and the presence of the prestress has been neglected in order to be closer to a realistic design. With the aim of estimating the performance of this approximated cloak, a Finite Element code is implemented, based on a sub-parametric technique. The tool allows the investigation of the sensitivity of specific stiffness parameters that may be difficult to match in a real cloak design. Moreover, the Finite Element code is extended to investigate a meta-plate interacting with a Winkler foundation, to analyse how the substrate modulus transforms in the cloak region. This second topic of the Thesis may find applications in the realization of approximated invisibility cloaks, which can be employed to reduce the destructive effects of earthquakes on civil structures or to shield mechanical components from unwanted vibrations.
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7

Chen, Yaming. "Dynamical properties of piecewise-smooth stochastic models." Thesis, Queen Mary, University of London, 2014. http://qmro.qmul.ac.uk/xmlui/handle/123456789/9129.

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Анотація:
Piecewise-smooth stochastic systems are widely used in engineering science. However, the theory of these systems is only in its infancy. In this thesis, we take as an example the Brownian motion with dry friction to illustrate dynamical properties of these systems with respect to three interesting topics: (i) weak-noise approximations, (ii) first-passage time (FPT) problems and (iii) functionals of stochastic processes. Firstly, we investigate the validity and accuracy of weak-noise approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example the Brownian motion with pure dry friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided that the singularity of the path integral is treated with some heuristics. We also consider a smooth regularisation of this piecewise-constant SDE and study to what extent this regularisation can rectify some of the problems encountered in the non-smooth case. Secondly, we provide analytic solutions to the FPT problem of the Brownian motion with dry friction. For the pure dry friction case, we find a phase transition phenomenon in the spectrum which relates to the position of the exit point and affects the tail of the FPT distribution. For the model with dry and viscous friction, we evaluate quantitatively the impact of the corresponding stick-slip transition and of the transition to ballistic exit. We also derive analytically the distributions of the maximum velocity till the FPT for the dry friction model. Thirdly, we generalise the so-called backward Fokker-Planck technique and obtain a recursive ordinary differential equation for the moments of functionals in the Laplace space. We then apply the developed results to analyse the local time, the occupation time and the displacement of the dry friction model. Finally, we conclude this thesis and state some related unsolved problems.
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8

Kubin, Ingrid, and Laura Gardini. "Border Collision Bifurcations in Boom and Bust Cycles." WU Vienna University of Economics and Business, 2012. http://epub.wu.ac.at/3490/1/wp137.pdf.

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Анотація:
Boom and bust cycles are widely documented in the literature on industry dynamics. Rigidities and delays in capacity adjustment in combination with bounded rational behavior have been identified as central driving forces. We construct a model that features only these two elements and we show that this is indeed sufficient to reproduce some stylized facts of a boom and bust cycle. The bifurcation diagrams summarizing the dynamic behavior reveal complex cycles and in particular also abrupt changes in the nature of these cycles. We apply new insights from the mathematical theory of piecewise smooth dynamic systems - in particular, results from the theory of border collision bifurcations - and show that the very existence of borders such as capacity constraints or nonnegativity constraints may lie behind abrupt changes in the dynamic behavior of economic variables. (author's abstract)
Series: Department of Economics Working Paper Series
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Wong, Chi Hong. "Border collision bifurcations in piecewise smooth systems." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/border-collision-bifurcations-in-piecewise-smooth-systems(1f2b9467-2c95-471b-82af-993b99d858ab).html.

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Piecewise smooth maps appear as models of various physical, economical and other systems. In such maps bifurcations can occur when a fixed point or periodic orbit crosses or collides with the border between two regions of smooth behaviour as a system parameter is varied. These bifurcations have little analogue in standard bifurcation theory for smooth maps and are often more complex. They are now known as "border collision bifurcations". The classification of border collision bifurcations is only available for one-dimensional maps. For two and higher dimensional piecewise smooth maps the study of border collision bifurcations is far from complete. In this thesis we investigate some of the bifurcation phenomena in two-dimensional continuous piecewise smooth discrete-time systems. There are a lot of studies and observations already done for piecewise smooth maps where the determinant of the Jacobian of the system has modulus less than 1, but relatively few consider models which allow area expansions. We show that the dynamics of systems with determinant greater than 1 is not necessarily trivial. Although instability of the systems often gives less useful numerical results, we show that snap-back repellers can exist in such unstable systems for appropriate parameter values, which makes it possible to predict the existence of chaotic solutions. This chaos is unstable because of the area expansion near the repeller, but it is in fact possible that this chaos can be part of a strange attractor. We use the idea of Markov partitions and a generalization of the affine locally eventually onto property to show that chaotic attractors can exist and are fully two-dimensional regions, rather than the usual fractal attractors with dimension less than two. We also study some of the local and global bifurcations of these attracting sets and attractors.Some observations are made, and we show that these sets are destroyed in boundary crises and some conditions are given.Finally we give an application to a coupled map system.
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Park, Youngmin. "Infinitesimal Phase Response Curves for Piecewise Smooth Dynamical Systems." Case Western Reserve University School of Graduate Studies / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=case1370643724.

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Книги з теми "Piecewise-smooth dynamics"

1

Glendinning, Paul, and Mike R. Jeffrey. An Introduction to Piecewise Smooth Dynamics. Edited by Elena Bossolini, J. Tomàs Lázaro, and Josep M. Olm. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23689-2.

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Laurea, Mario di Bernardo, Alan R. Champneys, Christopher J. Budd, and Piotr Kowalczyk, eds. Piecewise-smooth Dynamical Systems. London: Springer London, 2008. http://dx.doi.org/10.1007/978-1-84628-708-4.

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M, Di Bernardo, ed. Piecewise-smooth dynamical systems: Theory and applications. London: Springer Verlag, 2008.

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Bifurcations in piecewise-smooth continuous systems. New Jersey: World Scientific, 2010.

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5

Erik, Mosekilde, ed. Bifurcations and chaos in piecewise-smooth dynamical systems. River Edge, N.J: World Scientific, 2003.

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6

Glendinning, Paul, Mike R. Jeffrey, J. Tomàs Lázaro, Josep M. Olm, and Elena Bossolini. An Introduction to Piecewise Smooth Dynamics. Birkhäuser, 2019.

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7

Bernardo, Mario, Chris Budd, Alan Richard Champneys, and Piotr Kowalczyk. Piecewise-Smooth Dynamical Systems: Theory and Applications. Springer, 2008.

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8

Bernardo, Mario, Chris Budd, Alan Richard Champneys, and Piotr Kowalczyk. Piecewise-smooth Dynamical Systems: Theory and Applications. Springer, 2010.

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9

Bernardo, M. di, C. J. Budd, P. Kowalczyk, and Alan Richard Champneys. Piecewise-smooth Dynamical Systems: Theory and Applications (Applied Mathematical Sciences). Springer, 2007.

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10

The Octagonal PETs. American Mathematical Society, 2014.

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Частини книг з теми "Piecewise-smooth dynamics"

1

Glendinning, Paul, and Mike R. Jeffrey. "Piecewise-smooth Flows." In An Introduction to Piecewise Smooth Dynamics, 3–53. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23689-2_1.

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2

Glendinning, Paul, and Mike R. Jeffrey. "Piecewise-smooth Maps." In An Introduction to Piecewise Smooth Dynamics, 55–121. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23689-2_2.

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3

Piltz, Sofia H. "Smoothing a Piecewise-Smooth: An Example from Plankton Population Dynamics." In Trends in Mathematics, 147–51. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55642-0_26.

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4

Brandão, P., J. Palis, and V. Pinheiro. "On the Statistical Attractors and Attracting Cantor Sets for Piecewise Smooth Maps." In New Trends in One-Dimensional Dynamics, 31–50. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16833-9_4.

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5

Gardini, Laura, and Iryna Sushko. "Bifurcations in Smooth and Piecewise Smooth Noninvertible Maps." In Difference Equations, Discrete Dynamical Systems and Applications, 83–128. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20016-9_4.

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Teixeira, Marco Antonio, and Otávio M. L. Gomide. "Generic Singularities of 3D Piecewise Smooth Dynamical Systems." In Advances in Mathematics and Applications, 373–404. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94015-1_15.

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Avrutin, Viktor, and Iryna Sushko. "A Gallery of Bifurcation Scenarios in Piecewise Smooth 1D Maps." In Global Analysis of Dynamic Models in Economics and Finance, 369–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29503-4_14.

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Martins, Ricardo M., and Durval J. Tonon. "The Chaotic Behavior of Piecewise Smooth Dynamical Systems on Torus and Sphere." In Trends in Mathematics, 125–28. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55642-0_22.

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9

Ueta, Tetsushi, Tohru Kawabe, Guanrong Chen, and Hiroshi Kawakami. "Calculation and Control of Unstable Periodic Orbits in Piecewise Smooth Dynamical Systems." In Chaos Control, 321–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44986-7_14.

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10

Na, Jing, Qiang Chen, and Xuemei Ren. "Adaptive Control for Manipulation Systems With Discontinuous Piecewise Parametric Friction Model." In Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics, 93–105. Elsevier, 2018. http://dx.doi.org/10.1016/b978-0-12-813683-6.00008-8.

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Тези доповідей конференцій з теми "Piecewise-smooth dynamics"

1

Vestroni, Fabrizio, Paolo Casini, and Oliviero Giannini. "Nonlinear Dynamics of Piecewise Smooth Systems and Damage Identification." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48901.

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This paper addresses the study of the nonlinear dynamics of non-smooth systems representative of beams with breathing cracks. The aim is to use the nonlinear characteristics of the system response to identify the damage in cracked structures that behave similarly to bilinear systems and hence exhibit nonlinear phenomena in the dynamic response even for low damage levels. The idea is supported by the study of a piecewise smooth 2-DOF model where a wide variety of nonlinear phenomena has been evidenced, which include among others the bifurcations of super-abundant modes and a number of resonances greater than the system degrees of freedom. All these phenomena are strongly dependent on the stiffness discontinuity which is governed by the damage parameter. A novel method able to detect crack severity and position through measurements of the system nonlinear response has been developed and a cantilever beam with a breathing crack is considered as a numerical test case. The inverse procedure is tested by identifying the position and depth of a crack using pseudo-experimental data; the results show a strong robustness of the method even in the case when the data are affected by measurement errors.
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2

Saunders, B., R. Vasconcellos, Robert Kuether, and A. Abdelkefi. "Insights on the dynamics of piecewise-smooth oscillators with continuous representations." In Proposed for presentation at the NODYCON 2021 held February 16-19, 2021. US DOE, 2021. http://dx.doi.org/10.2172/1844047.

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3

Gall, Walter, Ying Zhou, and Joseph Salisbury. "Synchronization of a Network With Piecewise-Linear Dynamics." In ASME 2010 Dynamic Systems and Control Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/dscc2010-4230.

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We consider two and three phase-oscillators as in the Kuramoto model of coupled oscillators, replacing the sine wave interaction with a sawtooth wave. We show that for the case of non-uniform input-symmetric coupling strengths, the non-smooth, piecewise-linear dynamics synchronizes when the coupling strengths are large enough to overcome the differences in the natural frequencies of the oscillators. Stability is analyzed separately in the regions where the dynamics is linearized. These regions are separated by the switching boundaries where the vector field is discontinuous.
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4

Fedonyuk, Vitaliy, and Phanindra Tallapragada. "The Stick-Slip Motion of a Chaplygin Sleigh With a Piecewise Smooth Nonholonomic Constraint." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9820.

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The Chaplygin sleigh is a canonical problem of mechanical systems with nonholonomic constraints, which arises due to the role of friction. The motion of the cart has often been studied under the assumption that the magnitude of friction is as high as necessary to prevent slipping. We relax this assumption by setting a maximum finite value to the friction. The Chaplygin sleigh is then under a piecewise smooth nonholonomic constraint and transitions between ‘slip’ and ‘stick’ modes. We investigate these transitions and the resulting non smooth dynamics of the system. Further more the piecewise smooth constraint offers the possibility of controlling the speed of the sleigh and we investigate this with numerical simulations.
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5

Iklódi, Zsolt, Xavier Beudaert, and Zoltan Dombovari. "On the Modelling Bases of In-Motion Dynamic Characterization of Flexible Structures Subject to Friction and Position Control Delay." In ASME 2022 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/detc2022-90924.

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Abstract This article presents a characterisation technique of in-motion machine dynamics based on the principles of numerical continuation. A linear two degree of freedom mechanical model is considered, representing e.g. a flexible moving column of a machine tool, and is subjected to a non-smooth friction and a delayed feedback drive control force, resulting in a model governed by a system of piecewise-smooth delay differential equations. By applying harmonic forcing to the system, periodic solutions can be found, through the continuation of which, an accurate vibratory characterisation of in-motion machine dynamics can be acquired. In the continuation routine, spectral collocation techniques were employed to formulate the discretized boundary value problem of piecewise-smooth periodic orbits, and the pseudo-arclength method was implemented. Special care was attributed to the detection of grazing and sliding bifurcations, and the continuation routine was also extended to allow continuation of these critical points.
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Nguyen, Kim D., and Harry Dankowicz. "Principles of Dynamics for Design Applied to a Brush-Belt Material-Transfer System." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34431.

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This paper considers the performance characteristics of a brush-based material-transfer system, and the frictional interactions that result from the presence of particulate contaminants. The analysis of the dynamics of spherical objects transported through a cartridge by the brush is applied to isotropic and anisotropic belt designs. Experimental measurements of the load on individual objects, obtained using an instrumented cantilever, are compared with the predictions from a heuristic model, as well as preliminary observations from a qualitative bifurcation analysis of a piecewise-smooth dynamical system, in which a spring-loaded object slides along a looped belt with patches of distinct frictional properties.
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Wiebe, R., and T. Li. "Free Dynamics of Multi-Block Rocking Assemblies." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68014.

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Rocking systems are increasingly being investigated for use as base-isolators in structural engineering applications. Unfortunately these systems present complicated, piecewise defined, kinematic relationships between their generalized coordinates (usually the joint opening angles). This makes it difficult to obtain the governing equations, even for the dynamics between rocking/impact events. This paper seeks to address this through a systematic formulation of the governing equations of rocking post-tensioned assemblies with any number of blocks under base motion. The results are limited to the smooth dynamics between rocking events, and thus, although an important step, they do not give the complete description of rocking systems. The formulation utilizes the Euler-Lagrange equation to model the dynamics, with the constraint that all rocking occurs about the corners of the blocks.
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Yang, D. C. H., and Jui-Jen Chou. "Automatic Generation of Piecewise Constant Speed Motion for Multi-Axis Machines." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0337.

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Abstract This paper presents a general theory on the generation of smooth motion profiles for the coordinated motion of multi-axis manipulators with orthogonal regional structures. Motion with constant speed is important and required in many manufacturing processes, such as milling, welding, finishing and painting. In this paper, a piecewise constant speed profile is constructed by a sequence of Hermite cuves to form a composite Hermite curve in parametric domain. Due to the continuity of acceleration in the proposed speed profile, it generates relatively better product quality than traditional techniques. Besides, we also provide a method for the feasibility study of manufacture capability in terms of the given manipulator, the desired path, and the assigned speed. This includes the consideration of manipulator dynamics, actuator limitation, path geometry, jerk constraints and motion kinematics. The result is a general one and is applicable to all curves tracked by multi-axis manipulators with orthogonal regional structures.
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Beregi, Sándor, Dénes Takács, and David A. W. Barton. "Hysteresis Effect in the Nonlinear Stability of Towed Wheels." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67722.

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In this paper the dynamics of towed elastic wheels are studied with the help of the brush tyre model. To calculate the lateral deformation of the contact patch centre-line distributed time-delay is taken into account for the rolling parts, whereas parabolic limits are used to determine the deformation in case of side-slip. After linear stability analysis of the rectilinear motion the limit cycles of the non-smooth time-delayed system are calculated with the method of numerical collocation. With the help of bifurcation diagrams it is demonstrated how the periodic orbits develop from the linear stability boundary in a structure characteristic of piecewise-smooth systems. Moreover, it is shown that the contact memory effect and the dry friction yield bistable parameter ranges besides the linearly unstable domains. Namely, for one particular towing velocity a stable equilibrium corresponding to straight-line motion and a stable periodic orbit coexist resulting a hysteresis effect in the stability of the straight-line motion.
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Kong, Nathan J., George Council, and Aaron M. Johnson. "iLQR for Piecewise-Smooth Hybrid Dynamical Systems." In 2021 60th IEEE Conference on Decision and Control (CDC). IEEE, 2021. http://dx.doi.org/10.1109/cdc45484.2021.9683506.

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