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Register a new userScaling law of transient lifetime of chimera states under dimension-augmenting perturbations
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Chimera states arising in the classic Kuramoto system of two-dimensional phase coupled oscillators are transient but they are long transients in the sense that the average transient lifetime grows exponentially with the system size. For reasonably large systems, e.g., those consisting of a few hundreds oscillators, it is infeasible to numerically calculate or experimentally measure the average lifetime, so the chimera states are practically permanent. We find that small perturbations in the third dimension, which make system slightly three-dimensional, will reduce dramatically the transient lifetime. In particular, under such a perturbation, the practically infinite average transient lifetime will become extremely short, because it scales with the magnitude of the perturbation only logarithmically. Physically, this means that a reduction in the perturbation strength over many orders of magnitude, insofar as it is not zero, would result in only an incremental increase in the lifetime. The uncovered type of fragility of chimera states raises concerns about their observability in physical systems.
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We investigate two types of chimera states, i.e., patterns consisting of coexisting spatially separated domains with coherent and incoherent dynamics, in ring networks of Stuart-Landau oscillators with symmetry-breaking coupling, under the influence of noise. Amplitude chimeras are characterized by temporally periodic dynamics throughout the whole network, but spatially incoherent behavior with respect to the amplitudes in a part of the system; they are long-living transients. Chimera death states generalize chimeras to stationary inhomogeneous patterns (oscillation death), which combine spatially coherent and incoherent domains. We analyze the impact of random perturbations, addressing the question of robustness of chimera states in the presence of white noise. We further consider the effect of symmetries applied to random initial conditions.
We study the dynamics of mobile, locally coupled identical oscillators in the presence of coupling delays. We find different kinds of chimera states, in which coherent in-phase and anti-phase domains coexist with incoherent domains. These chimera states are dynamic and can persist for long times for intermediate mobility values. We discuss the mechanisms leading to the formation of these chimera states in different mobility regimes. This finding could be relevant for natural and technological systems composed of mobile communicating agents.
Chimera states in one-dimensional nonlocally coupled phase oscillators are mostly assumed to be stationary, but breathing chimeras can occasionally appear, branching from the stationary chimeras via Hopf bifurcation. In this paper, we demonstrate two types of breathing chimeras: The type I breathing chimera looks the same as the stationary chimera at a glance, while the type II consists of multiple coherent regions with different average frequencies. Moreover, it is shown that the type I changes to the type II by increasing the breathing amplitude. Furthermore, we develop a self-consistent analysis of the local order parameter, which can be applied to breathing chimeras, and numerically demonstrate this analysis in the present system.
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.
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