Effects of external global harmonic influence on chimera states
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ORIGINAL PAPER
Effects of external global harmonic influence on chimera states Igor A. Shepelev
· Tatiana E. Vadivasova
Received: 27 May 2020 / Accepted: 1 August 2020 © Springer Nature B.V. 2020
Abstract The effects of the global harmonic force on an ensemble of nonlocally coupled chaotic Rössler oscillators is studied. The autonomous ensemble without external force demonstrates a stable regime of chimera state. We have considered two types of the chimera states, namely phase chimera with a single incoherence cluster and combined chimera state with the incoherence clusters of the phase and amplitude chimeras. We have shown that even the sufficiently weak external influence leads to the qualitative changes in the spatiotemporal behavior of the ensemble under study. The diagram of regimes has been plotted in the plane of external signal parameters, where we detect regions with different dynamical regimes, induced by the external excitation. They are the spatiotemporal intermittence of structures, stable chimera states, stable regimes with a piecewise spatial profile, spatiotemporal chaos, complete chaotic synchronization and spatial incoherence. We have explored each of these regimes in detail and has found out that they are characterized by a certain distinctive range of the maximal Lyapunov exponent. We have found that the change of spatiotemporal behavior is not accompanied by the effects of locking the natural frequency or of suppression of selfoscillation by the external signal. I. A. Shepelev (B) · T. E. Vadivasova Saratov National Research State University, Astrakhanskaya Street 83, Saratov, Russia 410012 e-mail: [email protected] T. E. Vadivasova e-mail: [email protected]
Keywords Structural control · Spatiotemporal pattern formation · Oscillatory systems · External force · Rössler oscillator · Lyapunov Exponents · Nonlocal coupling · Chimera states
Introduction Investigation of oscillations, waves, synhronization effects and cluster structures in complex ensembles presents one of the crucial directions in nonlinear dynamics and its applications associated with the modelling processes in real complex systems [1–7]. Obviously, any complex system in nature, society, or technique is always subjected to influence of other systems and environment. This influence, depending on its random or regular nature, can be represented in mathematical models of the real systems by the external noise sources with certain statistical features or by an external regular force. The simplest case of the latter is an external harmonic signal with certain parameter values. The noise influence on complex systems is usually studied in relation to the phenomena of stochastic and coherent resonances [8–11] in ensembles of either bistable or excitable oscillators, accordingly. Besides, this influence is considered in the case of an effect of the synchronization of ensemble oscillators by the general stochastic signal [12]. The regular force can be represented periodic signals associated with periodic changing in the environment,
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