Analytical-Numerical Methods of Finding Hidden Oscillations in Multidimensional Dynamical Systems

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, and therefore one can readily identify it. In contrast, for a hidden attractor, the basin of attraction does not intersect with small 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. In this paper, we propose a new efficient analytical-numerical method for the study of hidden oscillations in multidimensional dynamical systems.