Numerical Verification Method of Existence of Connecting Orbits for Continuous Dynamical Systems

Shin'ichi Oishi (Department of Information and Computer Science, School of Science and Engineering, Waseda University, Japan)

Abstract: In this paper, a numerical method is presented for proving the existence and inclusion of connecting orbits of continuous dynamical systems described by parameterized nonlinear ordinary differential equations. Taking a certain second order nonlinear ordinary differential equaiton as an example, the existence of homoclinic bifurcation points is proved by the method.

Keywords: Connecting Orbits, Defining Equation of Stable-Manifolds, Numerical Verification of Existence of Nonlinear Boundary Value Problems