Homoclinic and Heteroclinic Orbits for a Liénard System - Rocsoreanu, Carmen; Sterpu, Mihaela (Journal of Informatics and Mathematical Sciences, 2018)
A 2D dynamical system exhibiting a double-zero bifurcation with symmetry of order two is considered. This bifurcation involves the presence in the parameter space of a curve corresponding either to double homoclinic or to heteroclinic bifurcations. In this paper we derive second order approximations for the homoclinic orbits and for the curve of homoclinic bifurcation values considering the system truncated up to five order terms and parameter-dependent coefficients. These approximations were obtained using the regular perturbation method. These formulae are applied to a Liénard system, which develops a double-zero bifurcation with symmetry of order two for some parameters values. Second order approximations for the heteroclinic orbits of this system are also given. The analytical results are very accurate and they are in good accordance with the numerical ones.