We report the exact analytical expression of the surface W4(a,b;λ)=0 defining stability domains for period-4 motions in the Hénon map, valid for arbitrary eigenvalues λ and parameters a and b. For λ=+1 (fold bifurcations) the expression reproduces all previous results and gives a new one. For...

We describe a novel mechanism for inducing traveling-wave attractors in rings of coupled maps. Traveling waves are easily produced when parameters controlling local dynamics vary from site to site. We also present some statistical results regarding the distribution of periodic time-evolutions.

We report surprisingly regular behaviors observed for a class 4 cellular automaton, the totalistic rule 20: starting from disordered initial configurations the automaton produces patterns which are periodic not only in time but also in space. This is the first evidence that different types of...

We investigate the propagation of bistable fronts in lattices of diffusively and advectively coupled cubic and quartic bistable maps, reporting the distribution of both stable states for asymmetric basins of attraction. The main effects of basin symmetry and local nonlinearities are obtained by...

We investigate the impact of bistability in the emergence of synchronization in networks of chaotic maps with delayed coupling. The existence of a single finite attractor of the uncoupled map is found to be responsible for the emergence of synchronization. No synchronization is observed when the...

We investigate the parameter space of two coupled quadratic (logistic) maps. Of special interest is the analytical characterization of the precursors leading to riddled basins. We delimit stability domains for orbits with the two lowest periods. In addition, we study the singularities of the...

We simulate a 2D coupled map lattice formed by individual units consisting of a multi-attractor quartic map. We show that the interesting recently discovered non-trivial collective behaviors (where macroscopic quantities show well-defined, usually regular, temporal evolution in spite of the...

We introduce a class of models composed by lattices of coupled complex-amplitude oscillators which preserve the norm. These models are particularly well adapted to investigate phenomena described by the nonlinear Schrödinger equation. The coupling between oscillators is parameterized by the...

We prove a theorem establishing a direct link between macroscopically observed periodic motions and certain subsets of intrinsically discrete orbits which are selected naturally by the dynamics from the skeleton of unstable periodic orbits (UPOs) underlying classical and quantum dynamics. As a...

We report exact analytical expressions locating the 0→1, 1→2 and 2→4 bifurcation curves for a prototypical system of two linearly coupled quadratic maps. Of interest is the precise location of the parameter sets where Naimark–Sacker bifurcations occur, starting from a non-diagonal...