nonlinear dynamical systems
localization of closed trajectories
stability of limit cycle
One of the important problems of nonlinear dynamic analysis is to study the qualitative behavior of solutions and stability of limit cycles of nonlinear differential equations. Large applied interest differential systems with the convex (concave) nonlinearity. We carried out estimation of the number of closed solutions of scalar non-autonomous differential equation with the appropriate terms of the concavity. Consider a dynamic system, described by the passer multidimensional nonlinear differential equations. For systems with a convex (concave) nonlinearity evaluated the number of closed trajectories. The necessary and sufficient conditions for existence and stability of the limiting cycles on the basis of N.E. Zhukovskij approach and generalization of A. Poincare – I. Bendixon theory are obtained.