The Structure of Synchronization Sets for Noninvertible Systems

Unidirectionally coupled systems where (x,y) maps to (f(x),g(x,y)) occur both naturally, and are used as tractable models of models with complex interactions. We analyze the structure and bifurcations of the attractor in the case the driving system is not invertible, and the response system is dissipative. We discuss both cases in which the driving system is a map, and a strongly dissipative flow. Although this problem was originally motivated by examples of nonlinear synchrony, we show that the ideas presented can be used more generally to study the structure of attractors, and examine interactions between systems in networks

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