Heteroclinic Cycles in a Competitive Network

Abstract

The competitive threshold linear networks are recently developed and are typical examples of non-smooth systems that can be easily constructed. By its facility of manipulating they are used in several applications, but its dynamic (both local and global) is not completely understood. In this work, we take some threshold systems recently developed and by a simple modification in the parameter space, we obtain new global dynamic behaviour. Heteroclinic cycles and other remarkable scenarios of global bifurcation are reported.