Bifurcation of Periodic Oscillations Arising from a Closed Phase Curve in Systems with Odd Nonlinearities

The paper considers the problem of the emergence of limit cycles, arising from the closed phase curve of a two-parameter dynamical system, containing odd nonlinearities. An approach is proposed to study the corresponding bifurcation problem of cycles. The approach is based on the construction of operator equation, the bifurcation points problem of which is equivalent to the to the original cycles bifurcation problem. To study the operator equation, the method of small parameter is used. The formulas for the main asymptotics of the arising periodic solutions, leading to effective algorithms for studying the problem under consideration. As an application, the problem of bifurcation of limit cycles in the modified van der Pol equation is considered.