Sensitivity of Global Dynamics on the microscopic details of a network of dynamically coupled maps

Abstract

Here we analyze the behavior of dynamically coupled maps, based on those introduced in a series of papers by Ito and Kaneko (Phys. Rev. Lett. 88:028701, 2002 and Phys. Rev. E 67:046226, 2003). We show how the microscopic coupling mechanism changes the behavior of the system both by affecting the stability of fixed points and through a more subtle effect in the crossover behavior between different regions of the parameter space. This makes it necessary to choose very carefully the exact manner in which one couples maps if they are to be used as a general model of composite systems.