Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle–focus and Saddle Under Reversible Condition

In this paper, we study the dynamical behavior for a 4?dimensional reversible system near its heteroclinic loop connecting a saddle?focus and a saddle. The existence of infinitely many reversible 1?homoclinic orbits to the saddle and 2?homoclinic orbits to the saddle?focus is shown.

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