相关论文: Broken ergodicity and glassy behavior in a determi…
We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behaviour of some global observables, with typical times much longer than the times related to…
We study the dynamics of hierarchy of piecewise maps generated by one-parameter families of trigonometric chaotic maps and one-parameter families of elliptic chaotic maps of $\mathbf{cn}$ and $\mathbf{sn}$ types, in detail. We calculate the…
When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
Dynamics of coupled chaotic oscillators on a network are studied using coupled maps. Within a broad range of parameter values representing the coupling strength or the degree of elements, the system repeats formation and split of coherent…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
Systems where time evolution follows a multiplicative process are ubiquitous in physics. We study a toy model for such systems where each time step is given by multiplication with an independent random $N\times N$ matrix with complex…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
A chaotic network of size $N$ with delayed interactions which resembles a pseudo-inverse associative memory neural network is investigated. For a load $\alpha=P/N<1$, where $P$ stands for the number of stored patterns, the chaotic network…
The Lyapunov exponent for collective motion is defined in order to characterize chaotic properties of collective motion for large populations of chaotic elements. Numerical computations for this quantity suggest that such collective motion…
We consider the spectral form factor of random unitary matrices as well as of Floquet matrices of kicked tops. For a typical matrix the time dependence of the form factor looks erratic; only after a local time average over a suitably large…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
We show that under certain simple assumptions on the topology (structure) of networks of strongly interacting chaotic elements a phenomenon of long range action takes place, namely that the asymptotic (as time goes to infinity) dynamics of…
In a recent letter [Phys.Rev.Lett. {\bf 30}, 3269 (1995), chao-dyn/9510011], we reported that a macroscopic chaotic determinism emerges in a multistable system: the unidirectional motion of a dissipative particle subject to an apparently…
The robustness of the universality class concept of the chaotic transition was investigated by analytically obtaining its critical exponent for a wide class of maps. In particular, we extended the existing one-dimensional chaotic maps,…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion…