Multiparameter bifurcation in periodic integrodifference equations

Abstract

Integrodifference equations appear as popular discrete‐time growth‐dispersal models in theoretical ecology. For such applications, seasonal influences are well‐motivated but lead to a large number of system parameters. This paper provides a flexible and easy to verify sufficient criterion for multiparameter bifurcation of periodic solutions to periodic integrodifference equations. In terms of a “bunch theorem,” a generic condition to identify those directions is given, in which solution branches do bifurcate. Additionally, we show that symmetry properties of integrodifference equations extend to the bifurcating solution branches.