An analysis of front dynamics in discrete time and spatially extended systems with general bistable nonlinearity is presented. The spatial coupling given by the convolution distribution functions. It allows us to treat a unified way discrete, continuous or partly diffusive interactions. We prove existence fronts uniqueness their velocity. also that velocity depends continuously on parameters system. Finally, we show every initial configuration an interface between stable phases propagates...

We study the time evolution of interfaces in one-dimensional bistable extended dynamical systems with discrete time. The dynamics are governed by competition between a local piecewise affine mapping and any couplings given convolution function bounded variation. prove existence travelling wave interfaces, namely fronts, uniqueness corresponding selected velocity shape. This is shown to be propagating for interface, depend continuously on increase symmetry parameter nonlinearity. apply...

In an infinite one-dimensional coupled map lattice (CML) for which the local is piecewise affine and bistable, we study global orbits using a spatiotemporal coding introduced in previous work. The set of all fixed points first considered. It shown that, under some restrictions on parameters, latter Cantor set, introduce order to points’ existence. This also involves proof coexistence propagating fronts stationary structures. second part, analyze occur strong coupling splitting dynamics into...

Abstract Beyond the uncoupled regime, rigorous description of dynamics (piecewise) expanding coupled map lattices remains largely incomplete. To address this issue, we study repellers periodic chains linearly Lorenz-type maps which analyze by means symbolic dynamics. Whereas all codes are admissible for sufficiently small coupling intensity, when interaction strength exceeds a chain length independent threshold, prove that large bunch is pruned and an extensive decay follows suit topological...

The rotation number of orientation-preserving circle maps that are not necessarily surjective nor injective is discontinuous. In this paper we characterize the points discontinuity and relationship between its various possible values on a discontinuity. particular, show that, for each map corresponding to number, all orbits periodic after fixed iterates, entire range numbers at finite.

In the space of orientation-preserving circle maps that are not necessarily surjective nor injective, rotation number does vary continuously. Each map where one these discontinuities occurs is itself discontinuous and we can consider possible values when modify this only at its discontinuities. These always rational numbers obey a certain arithmetic relation. paper show in several examples relation totally characterizes on discontinuities, but also prove circumstances sufficient for characterization.

We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis their dynamics. The are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables represent gene expression levels. When compared other networks, these have an additional parameter which is identified as quantifying interaction delays. In spite simplicity, dynamics presents a rich variety behaviours. This phenomenology not limited model but extends...