相关论文: A Solvable Model for Spatiotemporal Chaos

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…

We investigate the structure of the invariant measure of space-time chaos by adopting an "open-system" point of view. We consider large but finite windows of formally infinite one-dimensional lattices and quantify the effect of the…

We propose a discrete time dynamical system (a map) as phenomenological model of excitable and spiking-bursting neurons. The model is a discontinuous two-dimensional map. We find condition under which this map has an invariant region on the…

The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map…

We continue the development of transfer operator techniques for expanding maps on a lattice coupled by general interaction functions. We obtain a spectral gap for an appropriately defined transfer operator, and, as corollaries, the…

We study a synchronization mechanism, based on one-way coupling of all-or-nothing type, applied to coupled map lattices with several different local rules. By analyzing the metric and the topological distance between the two systems, we…

We investigate the synchronization phenomenon in coupled chaotic map lattices where the couplings decay with distance following a power-law. Depending on the lattice size, the coupling strength and the range of the interactions, complete…

The correlation between the values of wavefunctions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the…

Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal"…

The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems has been proposed. The application of this method is illustrated by the consideration of two different systems: i) the fluid model…

We demonstrate that a unidirectional coupling between a pattern forming system and its replica induces complete synchronization of the slave to the master system onto a spatiotemporal chaotic state.

Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…

We discuss the spatiotemporal intermittency (STI) seen in coupled map lattices (CML-s). We identify the types of intermittency seen in such systems in the context of several specific CML-s. The Chat\'e-Manneville CML is introduced and the…

We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic…

We consider complete synchronization of identical maps coupled through a general interaction function and in a general network topology where the edges may be directed and may carry both positive and negative weights. We define mixed…

We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…

Spatially-periodic patterns are studied in nonlocally coupled Gross-Pitaevskii equation. We show first that spatially periodic patterns appear in a model with the dipole-dipole interaction. Next, we study a model with a finite-range…

We analyze the size limits of coupled map lattices with diffusive coupling at the crossover of low-dimensional to high-dimensional chaos. We investigate the existence of standing-wave-type periodic patterns, within the low-dimensional…

We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map…

We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…