Imperfect traveling chimera states induced by local synaptic gradient coupling

In this paper we report the occurrence of chimera patterns in a network of neuronal oscillators, which are coupled through {\it local}, synaptic {\it gradient} coupling. We discover a new chimera pattern, namely the {\it imperfect traveling chimera} where the incoherent traveling domain spreads into the coherent domain of the network. Remarkably, we also find that chimera states arise even for {\it one-way} local coupling, which is in contrast to the earlier belief that only nonlocal, global or nearest neighbor local coupling can give rise to chimera; this find further relaxes the essential connectivity requirement of getting a chimera state. We choose a network of identical bursting Hindmarsh-Rose neuronal oscillators and show that depending upon the relative strength of the synaptic and gradient coupling several chimera patterns emerge. We map all the spatiotemporal behaviors in parameter space and identify the transitions among several chimera patterns, in-phase synchronized state and global amplitude death state.Comment: 8 pages, 9 figures,submitted for publicatio

Controlling Chimeras

Coupled phase oscillators model a variety of dynamical phenomena in nature and technological applications. Non-local coupling gives rise to chimera states which are characterized by a distinct part of phase-synchronized oscillators while the remaining ones move incoherently. Here, we apply the idea of control to chimera states: using gradient dynamics to exploit drift of a chimera, it will attain any desired target position. Through control, chimera states become functionally relevant; for example, the controlled position of localized synchrony may encode information and perform computations. Since functional aspects are crucial in (neuro-)biology and technology, the localized synchronization of a chimera state becomes accessible to develop novel applications. Based on gradient dynamics, our control strategy applies to any suitable observable and can be generalized to arbitrary dimensions. Thus, the applicability of chimera control goes beyond chimera states in non-locally coupled systems

Persistent chimera states in nonlocally coupled phase oscillators

Chimera states in the systems of nonlocally coupled phase oscillators are considered stable in the continuous limit of spatially distributed oscillators. However, it is reported that in the numerical simulations without taking such limit, chimera states are chaotic transient and finally collapse into the completely synchronous solution. In this paper, we numerically study chimera states by using the coupling function different from the previous studies and obtain the result that chimera states can be stable even without taking the continuous limit, which we call the persistent chimera state.Comment: To be published in Physical Review E (Rapid Communication), 5 pages, 7 figure

Spiral wave chimeras in locally coupled oscillator systems

The recently discovered chimera state involves the coexistence of synchronized and desynchronized states for a group of identical oscillators. This fascinating chimera state has until now been found only in non-local or globally coupled oscillator systems. In this work, we for the first time show numerical evidence of the existence of spiral wave chimeras in reaction-diffusion systems where each element is locally coupled by diffusion. This spiral wave chimera rotates inwardly, i.e., coherent waves propagate toward the phase randomized core. A continuous transition from spiral waves with smooth core to spiral wave chimeras is found as we change the local dynamics of the system. Our findings on the spiral wave chimera in locally coupled oscillator systems largely improve our understanding of the chimera state and suggest that spiral chimera states may be found in natural systems which can be modeled by a set of oscillators indirectly coupled by a diffusive environment.Comment: 5 pages, 5 figure