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...

In number theory, “units” are very special numbers characterized by having their norm equal to unity. So, in the real quadratic field Z (√3) the number of −2 + √3 ≅ −0.2679491924… is a unit because (−2 + √3) (−2 - √3) = 1. In this paper we determine precisely the...

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...

By varying real parameters, unstable complex orbits may become stable over wide parameter ranges. Thus, phase diagrams obtained by analyzing solely the stability of real solutions may be incomplete.

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 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...