The study of temporal chaos in low-dimensional systems, some of which can be described by low-dimensional maps @1,2#, was extremely beneficial for the understanding of turbulence. In 1984 coupled map lattices ~CMLs! were introduced into the physical literature as a tool for studying spatiotemporal chaos in spatially extended, i.e., highdimensional systems @3#. They consist of spatially coupled ...

An analytical mechanism that support localized spatio-temporal chaos is provided. We consider a simple model-the Nagumo Kuramoto model-which contains the crucial ingredients for observing localized spatio-temporal chaos, namely, the spatio-temporal chaotic pattern and its coexistence with a uniform state. This model allows us to unveil the front dynamics and to show that it can be described by ...

‎in the following text for arbitrary $x$ with at least two elements‎, ‎nonempty countable set $gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map‎. ‎we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney‎, ‎exact dev...

A brief review of Rayleigh–Bénard studies performed all along the twentieth century is presented, with an emphasis on the transition to turbulence and the appropriate theoretical framework, relying on the strength of confinement effects and the distance to threshold, either dynamical systems for temporal chaos in the strongly confined case, or models of space-time chaos when confinement effects...

We consider the effects of parametric perturbation on the onset of chaos in different dynamical systems. Favoring or suppression of chaos was observed depending on the phase or the frequency of the periodic perturbation. A lowering of the threshold of chaos was observed in an electronic device simulating a Josephson-Junction model and the suppression of chaos was obtained in a bistable mechanic...

Nerve membranes respond to periodically forcing stim~ilation not only periodically but also chaotically, depending upon parameter values of the force. We review the forced chaos in nerve membranes and it8s modeling with a simple one-dimensional map. We also discuss possible information processing, or chaotic PDP (Parallel Distributed Processing) with spatio-temporal chaos in net,works composed ...

We discuss the occurrence of chimera states in networks of nonlocally coupled bistable oscillators, in which individual subsystems are characterized by the coexistence of regular (a fixed point or a limit cycle) and chaotic attractors. By analyzing the dependence of the network dynamics on the range and strength of coupling, we identify parameter regions for various chimera states, which are ch...

It has been suggested that rising bubbles in dense fluids resemble an inverted dripping faucet and that they undergo analogous period-doubling bifurcations to chaos. We present experimental results demonstrating that this analogy is weak because the dominant source of instability in the bubble train is inherently different mutual interactions between spatially separated bubbles as opposed to no...