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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,
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Nonlinearity of local dynamics promotes multi-chimeras
Chimera states are complex spatio-temporal patterns in which domains of
synchronous and asynchronous dynamics coexist in coupled systems of
oscillators. We examine how the character of the individual elements influences
chimera states by studying networks of nonlocally coupled Van der Pol
oscillators. Varying the bifurcation parameter of the Van der Pol system, we
can interpolate between regular sinusoidal and strongly nonlinear relaxation
oscillations, and demonstrate that more pronounced nonlinearity induces
multi-chimera states with multiple incoherent domains. We show that the
stability regimes for multi-chimera states and the mean phase velocity profiles
of the oscillators change significantly as the nonlinearity becomes stronger.
Furthermore, we reveal the influence of time delay on chimera patterns
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