Complex patterns generated by the time evolution of a one-dimensional digitalized coupled map lattice are quantitatively analyzed. A method for discerning complexity among the different patterns is implemented. The quantitative results indicate two zones in parameter space where the dynamics shows the most complex patterns. These zones are located on the two edges of an absorbent region where t...

The circle map in one and two dimensions is studied. Both its stability and synchronization , using a bounded control and persistence, are discussed. This work is expected to be applicable in ecology where spatial effects are known to be important. Also, it will be relevant to systems where delay effects are not negligible.

We describe the emergence of phase clustering and collective behaviors in an ensemble of chaotic coupled map lattices, due to a mean field interaction. This kind of interaction is responsible for the appearence of a collective state, wherein the mean field evolution of each lattice undergoes a periodic behavior in space. We analyze the transition to such a state in an ensemble of one-dimensiona...

Two-dimensional coupled map lattices display, in a specific parameter range, a stable phase (quasi-) periodic in both space and time. With small changes to the model parameters, this stable phase develops spontaneous eruptions of nonperiodic behavior. Although this behavior itself appears irregular, it can be characterized in a systematic fashion. In particular, parameter-independent features o...

In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we compare its dynamics with the one of the whole lattice. We conclude a good agreement between the two. The reduced model also allows to introduce an order parameter which combines the diffusion parameter ...

Existence of traveling wave solutions for some lattice differential equations is investigated. We prove that there exists c 0 ∗ > such that for each c c∗ ≥ , the systems under consideration admit monotonic nondecreasing traveling waves.

Chaotic evolution of structures in Coupled map lattice driven by identical noise on each site is studied (a structure is a group of neighbouring lattice–sites for whom values of dynamical variable follow certain predefined pattern). Number of structures is seen to follow a power–law decay with length of the structure for a given noise–strength. A novel phenomenon, which we call stochas-tic cohe...

and Applied Analysis 3 This paper is organized as follows. In Section 2, we give some preliminaries including a comparison principle. Then we prove uniqueness of traveling wave with nonzero speed in Section 3. 2. Preliminaries The following lemma can be easily deduced from 1.5 and 1.6 . Lemma 2.1. Let {ui,j}i,j∈Z be a solution of 1.1 – 1.6 . If c > 0 < 0 , then ui,j t → 0 → 1 as t → ∞ and ui,j ...

We propose a model for co-evolving ecosystems that takes into account two levels of description of an organism, for instance genotype and phenotype. Performance at the macroscopic level forces mutations at the microscopic level. These, in turn, affect the dynamics of the macroscopic variables. In some regions of parameter space, the system self-organises into a state with localised activity and...