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

We extend Lin’s method for use in the setting of parameter-dependent nonlinear functional dierential 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 nite dimensional bifurcation equation. As an application, we describe the codimension two orbit-ip bifurcation in the setting of MFDEs.

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