Hidden Oscillations in Dynamical Systems. 16 Hilbert’s Problem, Aizerman’s and Kalman’s Conjectures, Hidden Attractors in Chua’s Circuits

Abstract

The present survey is devoted to efficient methods for localization of hidden oscillations in dynamical systems. Their application to Hilbert’s sixteenth problem for quadratic systems, Aizerman’s problem, and Kalman’s problem on absolute stability of control systems, and to the localization of chaotic hidden attractors (the basin of attraction of which does not contain neighborhoods of equilibria) is considered. The synthesis of the describing function method with the applied bifurcation theory and numerical methods for computing hidden oscillations is described.