Li–Yorke chaos on one-dimensional map lattices

Controlling Spatiotemporal Chaos in One- and Two-Dimensional Coupled Logistic Map Lattices

A method of control of spatiotemporal chaos in lattices of coupled maps is proposed in this work. Forms of spatiotemporal perturbations of a system parameter are analytically determined for oneand twodimensional logistic map lattices with different kinds of coupling to stabilize chosen spatiotemporal states previously unstable. The results are illustrated by numerical simulation. Controlled tra...

Chaos in one-dimensional lattices under intense laser fields

A model is investigated where a monochromatic, spatially homogeneous laser field interacts with an electron in a one-dimensional periodic lattice. The classical Hamiltonian is presented and the technique of stroboscopic maps is used to study the dynamical behavior of the model. The electron motion is found to be completely regular only for small field amplitudes, developing a larger chaotic reg...

Dynamics of inhomogeneous one – dimensional coupled map lattices

We study the dynamics of one–dimensional discrete models of one–component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities (" defects ") are treated in terms of parameter difference in the corresponding maps. Two types of space defects are considered: periodic and localized. We elaborate analytic approach to obtain the r...

One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures.

One-dimensional dynamics for traveling fronts in coupled map lattices

Multistable coupled map lattices typically support traveling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile allows a reduction of the infinitely dimensional dynamics to a one-dimensional circle homeomorphism, whose rotation number gives the propagation velocity. The mode locking of the velocity with respect to the s...