Heteroclinic Bifurcation of Strongly Nonlinear Oscillator

Abstract

Analytical prediction of heteroclinic bifurcation of the strongly nonlinear oscillator is presented by using the extended normal form method. We consider the approximate periodic solution of the system subject to the quintic nonlinearity by introducing the undetermined fundamental frequency. For the occurrence of heteroclinicity, the bifurcation criterion is accomplished. It depends on the contact of the limit cycle with the saddle equilibrium. As is illustrated, the explicit application shows that the new results coincide very well with the results of numerical simulation when disturbing parameter is of arbitrary magnitude.