Switching homoclinic networks

Abstract

A heteroclinic network for an equivariant ordinary differential equation is called switching if each sequence of heteroclinic trajectories in it is shadowed by a nearby trajectory. It is called forward switching if this holds for positive trajectories. We provide an elementary example of a switching robust homoclinic network and a related example of a forward switching asymptotically stable robust homoclinic network. The examples are for five-dimensional equivariant ordinary differential equations.

Keywords:

• switching dynamics
• homoclinic cycle

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Corrigendum: Switching homoclinic networks