Title: Lin's method and homoclinic bifurcations for functional differential equations of mixed type

Authors: H. J. Hupkes and S. M. Verduyn Lunel

Issue: Volume 58 (2009), Issue 6, 2433-2488

Abstract: We extend Lin's method for use in the setting of parameter-dependent nonlinear functional differential equations of mixed type (MFDEs). We show that the presence of $M$-homoclinic and $M$-periodic solutions that bifurcate from a prescribed homoclinic connection can be detected by studying a finite dimensional bifurcation equation. As an application, we describe the codimension two orbit-flip bifurcation in the setting of MFDEs.