Coexistence of strange nonchaotic attractors and a special mixed attractor caused by a new intermittency in a periodically driven vibro-impact system

Nonsmooth systems are widely encountered in engineering fields. They have abundant dynamical phenomena, including some results on the complex dynamics in such systems under quasiperiodically forced excitations. In this work, we consider a quasiperiodically forced piecewise linear oscillator and show that strange nonchaotic attractors (SNAs) do exist in such nonsmooth systems. The generation and evolution mechanisms of SNAs are discussed. The torus-doubling, fractal, bubbling, and intermittency routes to SNAs are identified. The strange properties of SNAs are characterized with the aid of the phase sensitivity function, singular continuous spectrum, rational frequency approximation, and the path of the partial Fourier sum of state variables in a complex plane. The nonchaotic properties of SNAs are verified by the methods of maximum Lyapunov exponent and power spectrum.

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“…The literature offers overviews and further references for other routes, see e.g. [25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Birth of strange nonchaotic attractors in a piecewise linear oscillator

Duan

Zhou

et al. 2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Many experts have found abundant strange nonchaotic dynamical properties in quasiperiodically forced systems [2][3][4]. In the periodically forced vibro-impact systems, the strange nonchaotic dynamical phenomena are found near points of codimension-2 [5] and codimension-3 2 [6] bifurcations. In a nonsmooth system with border-collision bifurcations [7], the different mechanisms for the birth of SNAs are investigated.…”

Section: Introductionmentioning

confidence: 99%

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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“…Liu et al [19] studied the dynamics of a capsule system in various friction environments. Yue et al [20] focused on the coexistence of strange nonchaotic attractors (SNAs) and a novel mixed attractor in a periodically driven three-degree-of-freedom vibro-impact system with symmetry. However, few of them are combined with engineering practice.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling and analysis of vertical vibration reduction system for passenger train

Dong

Meng

Song

et al. 2021

mech

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Based on wheel-rail impact vibration and considering the body stiffness and natural damping, this paper builds a four-degree-of-freedom vibro-impact system model for passenger train’s vertical vibration reduction system. The Poincaré map of the system is determined by the analytic solution of the system derived from the motion differential equation of the multi-degree-of-freedom vibro-impact system combined with Newton's second law. It is found that the fork bifurcation, Hopf bifurcation and other dynamical behavior leading to Chaos when the system parameters are changed. On this basis, the dynamic parameters of the train are optimized to avoid chaos in the train operation, reduce the vertical vibration of the train, improve the stability and comfort of the train operation, and provide the theoretical basis for the active vibration reduction design of the train.

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Coexistence of strange nonchaotic attractors and a special mixed attractor caused by a new intermittency in a periodically driven vibro-impact system

Cited by 28 publications

References 76 publications

Birth of strange nonchaotic attractors in a piecewise linear oscillator

Birth of strange nonchaotic attractors in a piecewise linear oscillator

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

Dynamic modeling and analysis of vertical vibration reduction system for passenger train

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