Synchronizability of piecewise-linear maps

In this paper we discuss the phenomenon of synchronization of chaotic systems in the case of coupled piecewise linear (PWL) continuous and discontinuous one-dimensional maps. We present numerical results for two examples of coupled systems consisting of two PWL maps. We illustrate how the coupled system can achieve synchronization and discuss the nature of the bifurcation that occurs at a critical value of the coupling strength. We then determine this critical coupling using linear stability analysis. We discuss the effects of variation of the parameters of the PWL maps on the critical coupling and present different bifurcation scenarios obtained for different sets of values of these parameters. Finally, we discuss an extension of our work to the synchronizability of networks consisting of two or more PWL maps. We show how the synchronizability of a network of PWL maps can be improved by tuning the map parameters.