The role of nonlinear diiusion terms in the stability of periodic solutions in the regime of spatio temporal chaos is studied. The stabilization of unstable plane waves in the Complex Ginzburg Landau equation in weakly chaotic regimes such as phase turbulence and spatiotemporal intermittency or in strong chaotic ones like defect turbulence is demonstrated.
Coherence evolution of two food web models can be obtained under the stirring effect of chaotic advection. Each food web model sustains a three-level trophic system composed of interacting predators, consumers, and vegetation. These populations compete for a common limiting resource in open flows with chaotic advection dynamics. Here we show that two… (More)
We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers (R. (1994)) as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional decreases monoton-ically in time towards the plane wave attractors, as expected for a Lyapunov functional,… (More)
A two-dimensional earthquake model that consists of a single block resting upon a slowly moving rough surface and connected by two springs to rigid supports is studied. Depending on the elastic anisotropy and the friction force three generic regimes are possible: i) pure creep; ii) pure stick-slip motion; and iii) a mixed regime. In all cases the long-time… (More)
Coupled Complex Ginzburg-Landau equations describe generic features of the dynamics of coupled fields when they are close to a Hopf bifurcation leading to non-linear oscillations. We study numerically this set of equations and find, within a particular range of parameters, the presence of uniformly propagating localized objects behaving as coherent… (More)
We study the propagation of fronts in extended oscillatory reaction-diffusion systems that contain several coexisting limit cycles. In contrast with the variational behavior, fronts between regions oscillating in two different limit cycles are found to propagate not necessarily towards the region of the less stable limit cycle, but towards the regions of… (More)
We study the spatiotemporal dynamics, in one and two spatial dimensions, of two complex fields which are the two components of a vector field satisfying a vector form of the complex Ginzburg-Landau equation. We find synchronization and generalized synchronization of the spatiotemporally chaotic dynamics. The two kinds of synchronization can coexist… (More)
The stabilization of periodic solutions in the regime of spatiotemporal chaos through a diffusion parameter control is studied. We show that unstable plane waves in the Complex Ginzburg-Landau equation can be effectively stabilized in chaotic regimes such as phase turbulence and spatiotemporal intermittency or defect turbulence.