Simultaneous Bifurcation of Limit Cycles and Critical Periods

Abstract The present work introduces the problem of simultaneous bifurcation limit cycles and critical periods for a system polynomial differential equations in plane. simultaneity concept is defined, as well idea bi-weakness return map period function. Together with classical methods, we an approach which uses Lie bracket to address some cases. This used find cubic quartic Liénard systems, general quadratic family, linear plus homogeneous family. We finish illustrative example by solving