Related papers: Frozen spatial chaos induced by boundaries
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex…
The dynamics in weakly chaotic Hamiltonian systems strongly depends on initial conditions and little can be affirmed about generic behaviors. Using two distinct Hamiltonian systems, namely one particle in an open rectangular billiard and…
We study the dynamics of the front separating a spatio-temporally chaotic region from a stable steady region using a simple model applicable to periodically forced systems. In particular, we investigate both the coarsening of the front…
We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a non-monotonic sequential associative memory model. We succeed in deriving…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
This paper is concerned with Devaney chaos in non-autonomous discrete systems. It is shown that in its definition, the two former conditions, i.e., transitivity and density of periodic points, in a set imply the last one, i.e., sensitivity,…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…
A novel class of nonequilibrium phase-transitions at zero temperature is found in chains of nonlinear oscillators.For two paradigmatic systems, the Hamiltonian XY model and the discrete nonlinear Schr\"odinger equation, we find that the…
Dense cold atomic clouds have been shown to be similar to plasmas. Previous studies showed that such clouds exhibit instabilities induced by long-range interactions. However they did not describe the spatial properties of the dynamics. In…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
We propose a stochastic sampling approach to identify stability boundaries in general dynamical systems. The global landscape of Lyapunov exponent in multi-dimensional parameter space provides transition boundaries for stable/unstable…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…
This paper develops a theory of propagation of chaos for a system of weakly interacting particles whose terminal configuration is fixed as opposed to the initial configuration as customary. Such systems are modeled by backward stochastic…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…