Spatiotemporal chaos in coupled logistic maps

Abstract

The objective of this work is to investigate the spatiotemporal dynamics of coupled logistic maps. These maps are prototypes of high-dimensional dynamical systems and have been used to describe the evolution and pattern formation in different systems. Here, the logistic map lattice is coupled by a power law and, therefore, each map is influenced by other maps in its neighborhood. The Kolmogorov–Sinai entropy density is employed to quantify the complexity of system behavior, permitting a general qualitative understanding of different aspects of system dynamics. Three kinds of boundary conditions are treated and the influence of initial conditions is also of concern. Non-homogeneous maps are investigated, showing interesting aspects of spatiotemporal dynamics. The idea is to analyze the spatial interaction between two qualitative different types of behavior from a grid that is split into two parts. Numerical simulations show what types of conditions present a greater tendency to develop chaotic, periodic and synchronized responses. It should be highlighted that non-homogeneous grids have situations where a chaotic pattern can emerge from two periodic responses and also situations where a periodic pattern can emerge from chaos.