When I see the literature about the chimera state, it exists only in the network of coupled nonlinear oscillator. They define the chimera such as the existence of coherent state and in-coherent state simultaneously. My question is that, if an attractor of a system has both the coherent and incoherent state, should we call it as chimera state? Like some portion of the attractor is chaotic and rest becomes regular.
http://arxiv.org/abs/nlin/0504046
Chimera is where coherent and noncoherent oscillators appear together. Here coherent means "synchronous" and non coherent represents oscillators which are not synchronized. Therefore you need a group oscillators(N>2) which are connected in a specific way(say non local) to get chimera. It is not related to the single oscillator .
Thank you very much Chita. Can I ask like following. If I have attractor like a ring ball and half of the ring ball consist of chaotic trajectory and remaining half become regular behaviour like torus. Can I call it as chimera? The literal mean of chimera is co-existence of multiple state. Yes I agree, in network of oscillator it may be a synchronized state and unsynchronized state.
In chimera state, two types of behaviors i.e., coherent/synchronized and incoherent/desynchronized state emerge as one state of the network of the system. For a single initial condition, the system approaches asymptotically to either of the attractor. It may be a coherent/incoherent/ chaotic/quasiperiodic state. But for the same initial condition, the system could not posses more than one state simultaneously (they may coexist in phase space).
Yes I understand. But there are situations where both the state coexists for single initial condition. They repeat alternatively/periodically in time.
Dear All, This is (see figure) what I was talking about. You can see some portion of the attractor have regular structure and remaining of the become chaotic.
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