Bifurcation of Bounded Solutions of Impulsive Differential Equations

Electronic version of an article published as International Journal of Bifurcation and Chaos, Volume 26, No. 14, 2016, 1-20 doi:10.1142/S0218127416502424 © copyright World Scientific Publishing Company, http://dx.doi.org/10.1142/S0218127416502424In this article, we examine nonautonomous bifurcation patterns in nonlinear systems of impulsive differential equations. The approach is based on Lyapunov–Schmidt reduction applied to the linearization of a particular nonlinear integral operator whose zeroes coincide with bounded solutions of the impulsive differential equation in question. This leads to sufficient conditions for the presence of fold, transcritical and pitchfork bifurcations. Additionally, we provide a computable necessary condition for bifurcation in nonlinear scalar impulsive differential equations. Several examples are provided illustrating the results