Infinite Number of Parameter Regions With Fractal Nonchaotic Attractors in a Piecewise Map

Abstract

We identify a countable infinity of parameter regimes with strange nonchaotic attractors (SNAs). At the edge of each arc parameter area, there is an uncountable infinity of SNAs with torus intermittency. The mechanism for the creation of SNAs in different regime is induced by an [Formula: see text]-frequency quasiperiodic orbit through a quasiperiodic analog of saddle-node bifurcation (Type-[Formula: see text] intermittent route). We describe the transition between tori and SNAs by the largest Lyapunov exponent and phase diagram. These SNAs are characterized by the phase sensitivity exponents, rational approximations, singular-continuous spectra, and distribution of finite-time Lyapunov exponents.

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

“…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]. Zhang et al [39] have found the grazing bifurcation route to the strange nonchaotic attractors in the quasiperiodically forced interval map.…”

Birth of strange nonchaotic attractors in a piecewise linear oscillator

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

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

“…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].…”