Symbolic dynamics, synchronization and homoclinic bifurcations in a class of globally coupled maps

By using the method of symbolic dynamics, we discuss the global synchronization and homoclinic bifurcations in a class of globally coupled systems with piecewise affine local map. We derive by virtue of admissibility condition the region of coupling strength for which the coupled system is globally synchronized. Homoclinic bifurcations are also discussed by making use of the admissibility condition when the local system is the shift map.