The Kuramoto model of globally coupled phase oscillators is an essentially nonlinear dynamical system with a rich dynamics including synchronization and chaos.We study the Kuramoto model from the standpoint of bifurcation and chaos theory of low-dimensional dynamical systems. We find a chaotic attractor in the four-dimensional Kuramoto model and study its origin. The torus destruction scenario ...

The aim of this paper is to development a very strong cryptographic systems using hyperelliptic Curves and Complete Synchronization for a Bidirectional Chaotic systems based on Lorenz attractor. Also performance simulations of SISO and MIMO systems over fading channels produce a benefit of 16dB for BER=10e−6 once the wireless channel is ensured. Key-Words:Diffie-Hellman Key Exchange, -Public Ke...

Abstract. We study the spin dynamics of a long nanomagnet driven by an electrical current. In the case of only DC current, the spin dynamics has a sophisticated bifurcation diagram of attractors. One type of attractors is a weak chaos. On the other hand, in the case of only AC current, the spin dynamics has a rather simple bifurcation diagram of attractors. That is, for small Gilbert damping, w...

This paper presents basic theoretical results for partial constant return maps (PCRMs) from controlled manifold piecewise linear chaotic circuits. Applying the instantaneous state setting method to the circuit, the chaotic attractor is changed into various superstable periodic orbits corresponding to the PCRM. Using an efficient algorithm, an important example of the PCRM can be analyzed almost...

We study the properties of the distance between attractors in Random Boolean Networks, a prominent model of genetic regulatory networks. We define three distance measures, upon which attractor distance matrices are constructed and their main statistic parameters are computed. The experimental analysis shows that ordered networks have a very clustered set of attractors, while chaotic networks’ a...

Fluctuational transitions between two co-existing chaotic attractors, separated by a fractal basin boundary, are studied in a discrete dynamical system. It is shown that the mechanism for such transitions is determined by a hierarchy of homoclinic points. The most probable escape path from the chaotic attractor to the fractal boundary is found using both statistical analyses of fluctuational tr...

A chaotic attractor containing unstable periodic orbits with different numbers of unstable directions is said to exhibit unstable dimension variability (UDV). We present general mechanisms for the progressive development of UDV in uni- and bidirectionally coupled systems of chaotic elements. Our results are applicable to systems of dissimilar elements without invariant manifolds. We also quanti...

Chaotic attractors arising in physical systems are often nonhyperbolic. We compare two sources of nonhyperbolicity: (1) tangencies between stable and unstable manifolds, and (2) unstable dimension variability. We study the effects of noise on chaotic attractors with these nonhyperbolic behaviors by investigating the scaling laws for the Hausdorff distance between the noisy and the deterministic...

Recent work has considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. The existence of invariant subspace often relies on certain symmetry of the system, which is, however, a nongeneric property as system defects and small rand...

Kampis proposed the study of chaotic itinerancy, pointing out its significance in domains of cognitive science and philosophy. He discovered in the concept of chaotic itinerancy the possibility for a new dynamical approach that elucidates mental states with a physical basis. This approach may therefore provide the means to go beyond the connectionist approach. In accordance with his theory, we ...