Due to a diffusive nearest-neighbor coupling, phase-synchronized states can emerge in two-dimensional chaotic coupled map lattices. By defining a direction phase (like a spin with up or down direction) as the direction of two sequential iterations of the logistic map, we find several novel kinds of phase synchronization which correspond to four different regions in a phase diagram. For the phas...

Low-dimensional iterated map models have been widely used to study action potential dynamics in isolated cardiac cells. Coupled iterated map models have also been widely used to investigate action potential propagation dynamics in one-dimensional (1D) coupled cardiac cells, however, these models are usually empirical and not carefully validated. In this study, we first developed two coupled ite...

Coupled map lattices (CMLs), using two coupled logistic equations, have been extensively used to model the dynamics of two-patch ecological systems. Such studies have revealed that migration rate plays an important role in determining the dynamics of the system, particularly when the two maps differ in their intrinsic growth rate parameter, r. However, under more realistic assumptions, a metapo...

Previous works have been devoted to the study of two-dimensional noninvertible maps, obtained using a coupling between one-dimensional logistic maps. This paper is devoted to the study of a specific one, in order to complete previous results [5] [7], regarding the evolution of basins and attractors, when considering the tool of critical manifolds.

A simple algorithm is described to target any desired operation point for simple one-dimensional and two-dimensional dynamical systems. What makes the algorithm unique is the fact that it targets any desired point, not merely a stable/unstable fixed point of the dynamics. It is shown how the method may be applied to the logistic map and the Hénon map. Generalisations to the case of n-dimensiona...

It is investigated how a spatial quenched disorder modifies the dynamics of coupled map lattices. The disorder is introduced via the presence or absence of coupling terms among lattice sites. Two nonlinear maps have been considered embodying two paradigmatic dynamics. The Miller and Huse map can be associated with an Ising-type dynamics, whereas the logistic coupled maps is a prototype of a non...

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...