<p>In view of the growing interest in chimera patterns in nonlinear dynamical systems, occurring when a group of oscillators spontaneously separates into a synchronized and desynchronized subsystems, this paper describes preliminary studies of the possibility of creating such and related behaviors by three selected models of chemical oscillatory reactions: the simplified model of the Epstein-Orbán reaction, OREGONATOR, and AUTOCALATOR. In particular, the Orbán–Epstein process, involving the oscillatory oxidation of thiocyanate ions by hydrogen peroxide in the presence of catalytic amounts of Cu<sup>2+</sup> ions, remains a unique combination of the characteristics of homogeneous redox processes with the electrochemical properties of inert indicator electrodes, which show antiphase oscillation characteristics in potentiometric measurements, depending on the electrode material. The model calculations assumed a system of 10 reactors coupled in circular configuration. Their nearest-neighbor (local) coupling was assumed to be of either diffusive (bidirectional) or convective (unidirectional) nature, while their global coupling was realized by fixed initial parameters for all reactors. Transient, chimera-like patterns were observed for the Epstein-Orbán reaction model under diffusion coupling conditions and for the convective coupling of OREGONATORs, while AUTOCALATOR showed the weakest effect of both types of coupling on its dynamics. Also, the role of the non-local mode of the diffusive and convective couplings was outlined in additional simulations. The presented results constitute the next stage of the search for chimera patterns in model nonlinear chemical systems and may become a premise for their possible future experimental verification.</p> Graphical Abstract <p></p>

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Towards chimera states in the models of coupled chemical oscillators

  • Maria Popławska,
  • Marek Orlik

摘要

In view of the growing interest in chimera patterns in nonlinear dynamical systems, occurring when a group of oscillators spontaneously separates into a synchronized and desynchronized subsystems, this paper describes preliminary studies of the possibility of creating such and related behaviors by three selected models of chemical oscillatory reactions: the simplified model of the Epstein-Orbán reaction, OREGONATOR, and AUTOCALATOR. In particular, the Orbán–Epstein process, involving the oscillatory oxidation of thiocyanate ions by hydrogen peroxide in the presence of catalytic amounts of Cu2+ ions, remains a unique combination of the characteristics of homogeneous redox processes with the electrochemical properties of inert indicator electrodes, which show antiphase oscillation characteristics in potentiometric measurements, depending on the electrode material. The model calculations assumed a system of 10 reactors coupled in circular configuration. Their nearest-neighbor (local) coupling was assumed to be of either diffusive (bidirectional) or convective (unidirectional) nature, while their global coupling was realized by fixed initial parameters for all reactors. Transient, chimera-like patterns were observed for the Epstein-Orbán reaction model under diffusion coupling conditions and for the convective coupling of OREGONATORs, while AUTOCALATOR showed the weakest effect of both types of coupling on its dynamics. Also, the role of the non-local mode of the diffusive and convective couplings was outlined in additional simulations. The presented results constitute the next stage of the search for chimera patterns in model nonlinear chemical systems and may become a premise for their possible future experimental verification.

Graphical Abstract