We investigate activator–inhibitor systems in two spatial dimensions with a non-local coupling, for which the interaction strength decreases with the lattice distance as a power-law. By varying a single parameter we can pass from a local (Laplacian) to a global (all-to-all) coupling type. We...

Neuron activity presents two timescales, a fast one related to action-potential spiking, and a slow timescale in which bursting takes place. Bursting activity in neuron ensembles can be synchronized, meaning the adjustment of the bursting phases due to coupling. We investigated bursting...

We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to another basin in an arbitrarily fine scale, which...

We examine the existence of an invariant manifold in the phase space structure presented by a dissipative four-wave coupling. We show that, once in such manifold, the system preserves two quantities as time evolves: a quantity related to the energy of the system and another, related to the...

Numerical simulations of coupled map lattices with non-local interactions (i.e., the coupling of a given map occurs with all lattice sites) often involve a large computer time if the lattice size is too large. In order to study dynamical effects which depend on the lattice size we considered...

We considered a coupled chaotic logistic map lattice exhibiting the scale-free property: the outreach connectivity of each node obeys a power-law distribution. We analyzed a weak form of coherent spatio-temporal behavior (direction coherence) which presents features common to completely...

We investigate aspects of the spatio-temporal dynamics exhibited by a one-dimensional lattice of chaotic piecewise linear maps in a coupling prescription which includes both regular (nearest and next-to-nearest neighbors) and randomly chosen couplings. We discuss the conditions for the existence...

Spatially extended dynamical systems may exhibit intermittent behavior in both spatial and temporal scales, characterized by repeated conversions from spatially localized transient chaos into global laminar patterns. A simple model, yet retaining some features of more complex systems, consists...

We used numerical diagnostics to quantify spatial disorder, and its relation with temporal chaos, for a one-dimensional chain of coupled logistic maps with a coupling strength which varies with the lattice distance in a power-law fashion. The main tool is spatial return plots, whose properties...

We study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses. We propose a simple mechanism in which the nonlocal connections are included, through electrical and chemical synapses. In the latter case, we introduce a time delay which produces...