Related papers: Bifurcations and transitions in the quasiperiodica…
Aperiodic dynamics which is nonchaotic is realized on Strange Nonchaotic attractors (SNAs). Such attractors are generic in quasiperiodically driven nonlinear systems, and like strange attractors, are geometrically fractal. The largest…
Different mechanisms for the creation of strange non-chaotic dynamics in the quasiperiodically forced logistic map are studied. These routes to strange nonchaos are characterised through the behavior of the largest nontrivial Lyapunov…
Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I…
Intermittent strange nonchaotic attractors (SNAs) appear typically in quasiperiodically forced period-doubling systems. As a representative model, we consider the quasiperiodically forced logistic map and investigate the mechanism for the…
Different mechanisms for the creation of strange nonchaotic attractors (SNAs) are studied in a two-frequency parametrically driven Duffing oscillator. We focus on intermittency transitions in particular, and show that SNAs in this system…
A simple quasiperiodically forced one-dimensional cubic map is shown to exhibit very many types of routes to chaos via strange nonchaotic attractors (SNAs) with reference to a two-parameter $(A-f)$ space. The routes include transitions to…
Strange nonchaotic attractors (SNAs) are observed in quasiperiodically driven time--delay systems. Since the largest Lyapunov exponent is nonpositive, trajectories in two such identical but distinct systems show the property of {\it…
Strange nonchaotic attractors (SNAs), which are realized in many quasiperiodically driven nonlinear systems are strange (geometrically fractal) but nonchaotic (the largest nontrivial Lyapunov exponent is negative). Two such identical…
The probability distribution of finite-time Lyapunov exponents provides an important characterization of dynamical attractors. We study such distributions for strange nonchaotic attractors (SNAs) created through several different mechanisms…
We show that it is possible to devise a large class of skew--product dynamical systems which have strange nonchaotic attractors (SNAs): the dynamics is asymptotically on fractal attractors and the largest Lyapunov exponent is nonpositive.…
Strange nonchaotic attractors (SNAs) can be created due to the collision of an invariant curve with itself. This novel ``homoclinic'' transition to SNAs occurs in quasiperiodically driven maps which derive from the discrete Schr\"odinger…
This paper focusses attention on the strange nonchaotic attractors (SNA) of a quasiperiodically forced dynamical system. Several routes, including the standard ones by which the appearance of strange nonchaotic attractors takes place, are…
Strange nonchaotic attractors (SNAs) in noise driven systems are investigated. Before the transition to chaos, due to the effect of noise, a typical trajectory will wander between the periodic attractor and its nearby chaotic saddle in an…
We propose a general mechanism by which strange non-chaotic attractors (SNA) are created during the collision of invariant curves in quasiperiodically forced systems. This mechanism is first discussed on an heuristic level and by means of…
We study one-parameter families of quasi-periodically forced monotone interval maps and provide sufficient conditions for the existence of a parameter at which the respective system possesses a non-uniformly hyperbolic attractor. This is…
We study bifurcation mechanisms for the appearance of hyperchaotic attractors in three-dimensional diffeomorphisms, i.e., such attractors whose orbits have two positive Lyapunov exponents in numerical experiments. In order to possess this…
We study chaotic dynamics in a system of four differential equations describing the dynamics of five identical globally coupled phase oscillators with biharmonic coupling. We show that this system exhibits strange spiral attractors…
Non-smooth saddle-node bifurcations give rise to minimal sets of interesting geometry built of so-called strange non-chaotic attractors. We show that certain families of quasiperiodically driven logistic differential equations undergo a…
A transition from a smooth torus to a chaotic attractor in quasiperiodically forced dissipative systems may occur after a finite number of torus-doubling bifurcations. In this paper we investigate the underlying bifurcational mechanism…
The emergence of noise-induced chaos in a random logistic map with bounded noise is understood as a two-step process consisting of a topological bifurcation flagged by a zero-crossing point of the supremum of the dichotomy spectrum and a…