2017•Mathematica SlovacaOpen access

Homoclinic and heteroclinic motions in hybrid systems with impacts

Mehmet Onur Fen, Fatma Tokmak Fen

Abstract

Abstract In this paper, we present a method to generate homoclinic and heteroclinic motions in impulsive systems. We rigorously prove the presence of such motions in the case that the systems are under the influence of a discrete map that possesses homoclinic and heteroclinic orbits. Simulations that support the theoretical results are represented by means of a Duffing equation with impacts.

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Available abstract

Key concepts: Homoclinic orbit, Heteroclinic orbit, Heteroclinic cycle, Heteroclinic bifurcation, Duffing equation, Homoclinic bifurcation, Classical mechanics, Mathematical analysis