Dynamic analysis of the coupled logistic map redounds to know and predict the characteristics of high-dimension complex nonlinear system. Using the method combining calculation and experiment, the following conclusions are shown: (1) The boundary equation of the first bifurcation of the coupled logistic map in the parameter space is given out. (2) Chaotic patterns of the coupled logistic map ma...

We consider networks of chaotic maps with different network topologies. In each case, they are coupled in such a way as to generate synchronized chaotic solutions. By using the methods of control of chaos we are controlling a single map into a predetermined trajectory. We analyze the reaction of the network to such a control. Specifically we show that a line of one-dimensional logistic maps tha...

Abstract For the delayed logistic equation x n +1 = ax (1 − −2 ) it is well known that nontrivial fixed point locally stable for 1 &lt; a ⩽ ( <mml:...

The logistic coupled map lattices (LCML) have been widely investigated as well as their pattern dynamics. The patterns formation may depend on not only fluctuations of system parameters, but variation of the initial conditions. However, the mathematical discussion is quite few for the effect of initial values so far. The present paper is concerned with the pattern formation for a two-dimensiona...

Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of “causal” coupling (to spatially distant past states) or “non-causal” coupling (to spatially distant simultaneous states). In this contribution we show that globally stabl...

A wide range of coupled map lattices is shown to have identical pattern sequences. It is found that the wave type solutions in their respective pattern selection regimes scale linearly with the coupling range indicating the existence of a continuum limit. The findings are used to introduce a very simple novel type of spatially extended map which can serve as a representative for this class of c...