We consider a lattice of coupled logistic maps with periodic boundary condition. We prove that synchronization and almost synchronization occur for the case of 1D lattice with lattice size n = 2, 3, 4 provided the coupling strength c is chosen in a suitable open interval contained in [0, 12 ]. For the case of lattice size n ≥ 4, we also show the numerical results of (almost) synchronized chaoti...

A fundamental periodicity problem of chaotic trajectories in computer realization with finite computation precision is investigated systematically by taking single and coupled Logistic maps as examples. Low-dimensional chaotic trajectories have rather short periods even with double precision computation, while the period increases rapidly when the number of coupled maps increases. Empirical exp...

Models of neurons based on iterative maps allows the simulation of big networks of coupled neurons without loss of biophysical properties such as spiking, bursting or tonic bursting and with an affordable computational effort. These models are built over a phenomenological basis and are mainly implemented by the use of iterative two-dimensional maps that can present neuro-computational properti...

The paper investigates the conditions for full and partial synchronization in systems of coupled chaotic maps that include the presence of a major element, that is, an element that interacts with all the other elements of the system. We consider a system which consists of two globally coupled populations of one-dimensional maps that interact via a major element. The presence of this element can...

Abstract 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 the basin of infinity in an arbitrarily fine scale, what has serious consequences on the predictability of the final state for such a coupled ...