Multistability in a quasiperiodically forced piecewise smooth dynamical system

Li, Gaolei; Yuan, Yongna; Xie, Jin; Grebogi, Celso

doi:10.1016/j.cnsns.2019.105165

Cited by 22 publications

(13 citation statements)

References 39 publications

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“…The attractor does wrinkle in the transition which can be regarded as the precursor to SNAs. Papers [10][11][12][13] uncover multistability of the coexistence of SNAs and quasiperiodic attractors, which enriches the study of SNAs. The strange and nonchaotic properties of SNAs can be verified by numerical methods such as Lyapunov exponent, phase sensitivity, power spectrum, fractal dimension, spectral distribution functions, rational approximations, and so on [14][15][16].…”

Section: Introductionmentioning

confidence: 89%

Strange Nonchaotic Attractors in a Periodically Forced Piecewise Linear System With Noise

Yuan

Grebogi

et al. 2021

Fractals

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The study of strange nonchaotic attractors (SNAs) has been mainly restricted to quasiperiodically forced systems. At present, SNAs have also been uncovered in several periodically forced smooth systems with noise. In this work, we consider a periodically forced nonsmooth system and find that SNAs are created by a small amount of noise. SNAs can be generated in different periodic windows with weak noise perturbation. If the parameter is varied further from the chaotic range, a larger noise intensity is required to induce SNAs. Besides, noise-induced SNAs can be generated by the periodic attractors near the boundary crisis. In addition, with the increasing noise intensity, the intermittency between SNAs and periodic attractors can be induced by transient chaos. The characteristics of SNAs are analyzed by the Lyapunov exponent, power spectrum, singular continuous spectrum, spectral distribution functions, and finite time Lyapunov exponent.

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Section: Introductionmentioning

confidence: 89%

Strange Nonchaotic Attractors in a Periodically Forced Piecewise Linear System With Noise

Yuan

Grebogi

et al. 2021

Fractals

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“…Over the past decades, non-smooth dynamical systems have received a large amount of research interests of researchers from various fields [16][17][18]. For instance, a wide variety of systems in biology, physics, and engineering are described by piecewise-smooth dynamical systems [19][20][21][22][23][24][25][26][27] ) (…”

Section: Fake Floquet Multipliersmentioning

confidence: 99%

On the Computation of Floquet Multipliers for Periodic Solution in Piecewise-smooth Dynamical System

Lai,

Chen

2024

J. Phys.: Conf. Ser.

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The floquet multiplier is one of the most important indicators for the stability and bifurcation analysis for periodic solutions in nonlinear dynamical systems. Different from the well-established Floquet theory for the perturbation systems of smooth systems, much less has been understood in its counterpart for non-smooth systems. Here in this paper, we will report an unusual and interesting feature of the Floquet multipliers for piecewise-smooth dynamical systems. When the initial condition of the periodic solution is located at the boundary splitting the solution domain, the multipliers would be calculated falsely in certain circumstances, respectively, by a saltation matrix method or a direct numerical integration for the perturbation system. We elucidate the origin of the fake multipliers through perturbation analysis, and furthermore suggest an effective manner to avoid the miscalculation. This finding would be of fundamental significance to both the real-world applications and theory establishment of the Floquet theory in non-smooth systems

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“…In nonsmooth Chua's oscillators, some other routes to SNAs have been identified, e.g., multilayered bubbling route [28], formation and merging of bubbles route [29]. In the vibro-impact systems, SNAs are also verified by different bifurcations [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

“…Although SNAs of nonsmooth systems are common [28][29][30][31][32][33][34][35][36], bifurcations and mechanisms leading to SNAs have not been entirely clear. It is well known that SNAs via different routes may possess different properties so that SNAs can be applied to different areas .…”

Section: Introductionmentioning

confidence: 99%

Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map

Zhao

Zhang

2023

Chaos, Solitons & Fractals

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Multistability in a quasiperiodically forced piecewise smooth dynamical system

Cited by 22 publications

References 39 publications

Strange Nonchaotic Attractors in a Periodically Forced Piecewise Linear System With Noise

Strange Nonchaotic Attractors in a Periodically Forced Piecewise Linear System With Noise

On the Computation of Floquet Multipliers for Periodic Solution in Piecewise-smooth Dynamical System

Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map

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