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

Abstract

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.

Multiple tori intermittency routes to strange nonchaotic attractors in a quasiperiodically-forced piecewise smooth system

“…Duan et al confirmed that strange non-chaotic attractors do exist in non-smooth systems [35]. Li et al have studied the generative mechanism of SNAs in a quasiperiodic forced piecewise smooth system [36][37]. Cheng et al have found that the formation mechanism of strange nonchaotic attractors is induced by infinite many saddle-node bifurcations (Type-I intermittent path) [38].…”

Quantifying strange property of attractors in quasiperiodically forced systems

“…2(d). Example 2: The Ricker family with quasiperiodic excitation is considered [22], the skew product system F :…”

Double grazing bifurcation route in a quasiperiodically driven piecewise linear oscillator

“…By means of nonlinear dynamical analysis and numerical evidence, Zhang et al [22] found SNAs in the periodically driven noisy FHN neuron model. Li et al [23] considered a periodically forced nonsmooth system and found that noise-induced SNAs can be generated by periodic attractors near the boundary crisis. Shen et al [24] studied the mechanisms for the creation of strange nonchaotic attractors in a quasiperiodic forced piecewise logistic system, and uncovered the Heagy-Hammel routes, fractalization route and intermittent routes after the two coexisting tori collide.…”