We examine the problem of the dynamics of interfaces in a one-dimensional space-time discrete dynamical system. Two different regimes are studied: the non-propagating and the propagating one. In the first case, after proving the existence of such solutions, we show how they can be described using Taylor expansions. The second situation deals with the assumption of a travelling wave to follow th...

Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logistic function. The logistic model implies a replacement process, and the logistic substitution suggests non-linear dynamical behaviors such as bifurcation and chaos. Using mathematical transform and n...

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...

This paper presents a spiking neuron circuit with a triangular base signal. The circuit can output rich pulse-trains and the dynamics can be analyzed using a piecewise linear one-dimensional pulse-position map. Applying cross-switching to two neurons we construct a pulse-coupled system whose dynamics can be integrated into a composite map of the pulse position maps of two neurons. The composite...

In this paper we present local Sternberg conjugation theorems near attracting fixed points for lattice systems. The interactions are spatially decaying and not restricted to finite distance. conjugations obtained retain the same spatial decay. presence of resonances a polynomial normal form that also has properties.

We numerically demonstrate that collective bifurcations in two-dimensional lattices of locally coupled logistic maps share most of the defining features of equilibrium second-order phase transitions. Our simulations suggest that these transitions between distinct collective dynamical regimes belong to the universality class of Miller and Huse model with synchronous update [Marcq et al., Phys. R...

Though considerable effort has recently been devoted to hardware realization of one-dimensional chaotic systems, the influence of implementation inaccuracies is often underestimated and limited to non-idealities in the non-linear map. Here we investigate the consequences of sample-and-hold errors. Two degrees of freedom in the design space are considered: the choice of the map and the sample-an...