8 research outputs found
Hidden attractors in fundamental problems and engineering models
Recently a concept of self-excited and hidden attractors was suggested: an
attractor is called a self-excited attractor if its basin of attraction
overlaps with neighborhood of an equilibrium, otherwise it is called a hidden
attractor. For example, hidden attractors are attractors in systems with no
equilibria or with only one stable equilibrium (a special case of
multistability and coexistence of attractors). While coexisting self-excited
attractors can be found using the standard computational procedure, there is no
standard way of predicting the existence or coexistence of hidden attractors in
a system. In this plenary survey lecture the concept of self-excited and hidden
attractors is discussed, and various corresponding examples of self-excited and
hidden attractors are considered
Rare and hidden attractors in Van der Pol-Duffing oscillators
We study the dynamics of the single and coupled van der Pol-Duffing oscillators. Each oscillator is characterized by the multistability (the coexistence of attractors). Some of the coexisting attractors have very small basins of attraction (the rare ones) and some of them do not contain equilibria in their basin of attraction (the hidden ones). We perform the detailed bifurcation analysis of these attractors and investigate how this plethora of states influences the dynamics of the network of coupled oscillators. We have observed the cluster synchronization on different attractors as well as different types of chimera states