Emergence of patterns in driven and in autonomous spatiotemporal systems

Chaotic synchronization in large map networks

The chaotic synchronization in n-dimensional large map networks with local coupling and their size stabilities in the node number N-->infinity are studied analytically and numerically. The analytical results show that the chaotic synchronization is stable for N-->infinity in the presence of the external driving or global coupling. The numerical calculations show that, as the driving or global interaction strength increases from zero, the network states have the whole route: spatiotemporal chaotic state --> cluster chaotic synchronous state --> complete chaotic synchronous state --> spatiotemporal pattern --> spatiotemporal chaotic state.

Local versus global interactions in nonequilibrium transitions: A model of social dynamics

A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in the collective behavior of this system. Both for autonomous and external fields, disorder grows in the system when the probability of the elements to interact with the field is increased. There exists a threshold value of this probability beyond which the system is always disordered. The domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields. However, the zero field limit is discontinous. In the limit of vanishingly small probability of interaction with the field, autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone. We consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of Axelrod's model for cultural dissemination.

Synchronization in driven versus autonomous coupled chaotic maps

The phenomenon of synchronization occurring in a locally coupled map lattice subject to an external drive is compared to the synchronization process in an autonomous coupled map system with similar local couplings plus a global interaction. It is shown that chaotic synchronized states in both systems are equivalent, but the collective states arising after the chaotic synchronized state becomes unstable can be different in these two systems. It is found that the external drive induces chaotic synchronization as well as synchronization of unstable periodic orbits of the local dynamics in the driven lattice. On the other hand, the addition of a global interaction in the autonomous system allows for chaotic synchronization which is not possible in a large coupled map system possessing only local couplings.

Pattern formation in diffusive-advective coupled map lattices

We investigate pattern formation and evolution in coupled map lattices when advection is incorporated, in addition to the usual diffusive term. All patterns may be suitably grouped into five classes: three periodic, supporting static patterns and traveling waves, and two nonperiodic. Relative frequencies are determined as a function of all model parameters: diffusion, advection, local nonlinearity, and lattice size. Advection plays an important role in coupled map lattices, being capable of considerably altering pattern evolution. For instance, advection may induce synchronization, making chaotic patterns evolve periodically. As a byproduct we describe a practical algorithm for classifying generic pattern evolutions and for measuring velocities of traveling waves.