Prediction of Hidden Oscillations Existence in Nonlinear Dynamical Systems: Analytics and Simulation

Abstract

From a computational point of view, in nonlinear dynamical systems, attractors can be regarded as self-excited and hidden attractors. Self-excited attractors can be localized numerically by a standard computational procedure, in which after a transient process a trajectory, starting from a point of unstable manifold in a neighborhood of equilibrium, reaches a state of oscillation, therefore one can easily identify it. In contrast, for a hidden attractor, a basin of attraction does not intersect neighborhoods of equilibria. While classical attractors are self-excited, attractors can therefore be obtained numerically by the standard computational procedure, for localization of hidden attractors it is necessary to develop special procedures, since there are no similar transient processes leading to such attractors. This keynote lecture is devoted to affective analytical-numerical methods for localization of hidden oscillations in nonlinear dynamical systems and their application to well known fundamental problems and applied models.