We study a coupled map lattice model with two states: a simple xed point and spatio-temporal chaos. Preparing properly initial conditions, we investigate the dynamics of the interface between order and chaos. In the one-dimensional lattice regimes of irregular and regular front propagation behavior are observed and analyzed by introducing a local front map and a front Lyapunov exponent. Corresp...

This lecture defines formally the new concept of "edge of chaos" in a mathematically rigorous, explicit, and easily testable manner. The main result asserts that the edge of chaos is the Holy Grail that both Alan Turing and Stephen Smale had sought in vain. It is in fact the genesis of non-homogeneous spatial-temporal patterns and structures widely reported in complexity theory. 25.05.2012 Begi...

In problems where the temporal evolution of a nonlinear system cannot be followed, a method for studying the fluctuations of spatial patterns has been developed. That method is applied to well-known problems in deterministic chaos (the logistic map and the Lorenz model) to check its effectiveness in characterizing the dynamical behaviors. It is found that the indices μq are as useful as the Lya...

We uncover a coherence resonance near the Hopf bifurcation from chaos in coupled chaotic oscillators. At the bifurcation, a nearly periodic rotating wave becomes stable as the state of synchronous chaos is destabilized. We find that noise can induce the bifurcation and, more strikingly, it can enhance the temporal regularity of the wave pattern in the coupled system. This resonant phenomenon is...

We investigate the thermodynamic chaos of RN-AdS black holes immersed in Perfect Fluid Dark Matter by considering dynamical equations fluid system evolved spinodal region. Based on Melnikov method, it is shown that there exists a critical amplitude affects temporal chaos. And influence charge and state parameter investigated with specific initial temperature. Then, for inevitable spatial chaos,...

Deterministic chaos has an intriguing characteristic that definite deterministic dynamics produces erratic and long-term unpredictable behavior [1], [2]. Understanding of deterministic chaos has greatly progressed in the past 25 years, although the possibility of chaotic dynamics was demonstrated mathematically at least 100 years ago by Hadamard and Poincaré [3]. It is now well known that chaot...

Abstract Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review theory deterministic temporal chaos in plasmas discuss its link to intermittent observed space First, we chaos, intermittency, complexity Alfvén waves, parametric decay modulational wave–wave interactions, absence/presence noise. The transition f...

Highly connected recurrent neural networks often produce chaotic dynamics, meaning their precise activity is sensitive to small perturbations. What are the consequences of chaos for how such networks encode streams of temporal stimuli? On the one hand, chaos is a strong source of randomness, suggesting that small changes in stimuli will be obscured by intrinsically generated variability. On the...

The work is devoted to the analysis of dynamics of traveling waves in a chain of self-oscillators with period-doubling route to chaos. As a model we use a ring of Chua’s circuits symmetrically coupled via a resistor. We consider how complicated are temporal regimes with parameters changing influences on spatial structures in the chain. We demonstrate that spatial periodicity exists until transi...