Related papers: Fractalization of Torus Revisited as a Strange Non…
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…
We consider the dynamics of small perturbations of stable two-frequency quasiperiodic orbits on an attracting torus in the quasiperiodically forced Henon map. Such dynamics consists in an exponential decay of the radial component and in a…
Transition from quasiperiodicity with many frequencies (i.e., a high-dimensional torus) to chaos is studied by using $N$-dimensional globally coupled circle maps. First, the existence of $N$-dimensional tori with $N\geq 2$ is confirmed…
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…
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 bifurcation transition is studied for the onset of intermittency analogous to the Pomeau-Manneville mechanism of type-I, but generalized for the presence of a quasiperiodic external force. The analysis is concentrated on the…
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…
We observe the occurrence of a strange nonchaotic attractor in a periodically driven two-dimensional map, formerly proposed as a neuron model and a sequence generator. We characterize this attractor through the study of the Lyapunov…
In this work we report a new route to chaos from a resonance torus in a piecewise smooth non-invertible map of the plane into itself. The closed invariant curve defining the resonance torus is formed by the union of unstable manifolds of…
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…
We show that the nontwist phenomena previously observed in Hamiltonian systems exist also in time-reversible non-Hamiltonian systems. In particular, we study the two standard collision/reconnection scenarios and we compute the parameter…
In mesoscopic systems conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system with either fully chaotic or mixed phase space generically…
In this study, we investigate the occurrence of a three-frequency quasiperiodic torus in a three-dimensional Lotka-Volterra map. Our analysis extends to the observation of a doubling bifurcation of a closed invariant curve, leading to a…
We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.
This paper compares three different types of ``onset of chaos'' in the logistic and generalized logistic map: the Feigenbaum attractor at the end of the period doubling bifurcations; the tangent bifurcation at the border of the period three…
Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…
Understanding irreversibility in macrophysics from reversible microphysics has been the holy grail in statistical physics ever since the mid-19th century. Here the central question concerns the arrow of time, which boils down to deriving…
The stationary distribution of a fully chaotic system typically exhibits a fractal structure, which dramatically changes if the dynamical equations are even slightly modified. Perturbative techniques are not expected to work in this…
As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…