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.