Abstract:
The lecture gives an overview of recent development in the theory of hidden oscillations. A particular attention is given to the classification of attractors of dynamical systems proposed: the attractor is called “self-excited” if its basin contains an equilibrium in its closure and “hidden”, if it is not the case, respectively. This classification revealed links with some fundamental problems (the second part of Hilbert’s 16th problem on the number and mutual disposition of limit cycles, Aizerman and Kalman conjectures on the monostability of nonlinear systems) and also triggered the discovery of new hidden attractors in well-known physical and engineering models.