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| We describe chimera state phenomenon for networks of non-locally coupled oscillators, in which individual systems are bi-stable having one regular attractor (e.g. equilibrium) and one chaotic. By analyzing the dependence of the network dynamics on the range and strength of coupling, we obtain parameter regions for various chimera types, which are characterized by different type of chaotic behavior at the irregular part of chimera state.
Peculiar cases are (i) pure temporal chaos which means the chaotic synchronization of the irregular oscillators and (ii) pure spatial chaos when temporal dynamics remain regular (stationary or periodic) but the oscillators are 'randomly situated' along the spatial network coordinate(s). More typical is the situation (iii) when both evolutional and translational dynamical systems are chaotic, then space-temporal chaotic behavior for the irregular oscillators emerges; e.g. for the original chimeras found in complex GLU and the Kuramoto model. Various combinations of (i)-(iii) are also possible.
We demonstrate the phenomenon for networks of bi-stable units with different types of individual dynamics, including coupled maps (piece-wise linear and smooth) and coupled time-continuous systems of the Van der-Pol type. Parameter regions for various types of the chimera states are obtained and scenarios for transitions between them are analyzed. |
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