title: The structure of synchronization sets for noninvertible systems.
abstract: Unidirectionally coupled systems (x,y) --> (f(x),g(x,y)) occur naturally, and are used as tractable models of networks with complex interactions. We analyze the structure and bifurcations of attractors 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 coupled systems.
authors.affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204, USA.
authors.forename: Kresimir
authors.initials: K
authors.lastname: Josić
authors.forename: Evelyn
authors.initials: E
authors.lastname: Sander