On Bifurcation of Cycles at Infinity in Systems with Homogeneous Nonlinearities

In this article, the problem of bifurcation of cycles at infinity in dynamical systems with homogeneous nonlinearities of even order is studied. Sufficient conditions for such bifurcation are proposed, determined both by the principal linear part and by the characteristics of the nonlinearities. Asymptotic formulas are obtained, which allow describing the evolution of the emerging cycles as the system parameters change. As an application, the problem of bifurcation of cycles at infinity in a modified Rössler model is considered.