Existence tests for limiting cycles of second order differential equations

This work is devoted to finding limiting cycles in the vicinity of equilibria of second order nonlinear differential equations. We obtain new conditions for the coefficients of the equations ensuring the existence of a limiting cycle by employing the methods of qualitative analysis and computer modeling. We study the behavior of a singular point under variation of the parameters and we apply the Lyapunov stability theory. On the base of the obtained results, we make a sector partition of the plane. This partition allows us to predict the behavior of the solutions in various parts of the plane. We develop a package of computer programs for constructing a phase portrait in the corresponding domains.