Abstract

We investigate the formation of weak chimera states in modular networks of electrochemical oscillations during the electrodissulution of nickel in sulfuric acid. In experiment and simulation, we consider two globally coupled populations of highly nonlinear oscillators which are weakly coupled through a collective resistance. Without cross coupling, the system exhibits bistability between a one- and a two-cluster state, whose frequencies are distinct. For weak cross coupling and initial conditions for the one- and two-cluster states for populations 1 and 2, respectively, weak chimera dynamics are generated. The weak chimera state exhibits localized frequency synchrony: The oscillators in each population are frequency-synchronized while the two populations are not. The chimera state is very robust: The behavior is maintained for hundreds of cycles for the rather heterogeneous natural frequencies of the oscillators. The experimental results are confirmed with numerical simulations of a kinetic model for the chemical process. The features of the chimera states are compared to other previously observed chimeras with oscillators close to Hopf bifurcation, coupled with parallel resistances and capacitances or with a nonlinear delayed feedback. The experimentally observed synchronization patterns could provide a mechanism for generation of chimeras in biological systems, where robust response is essential.

Highlights

  • Synchronization of oscillatory chemical reactions is an important dynamical phenomenon with relevance to many physical and biological processes [1]

  • We report the occurrence of weak chimera states in a modular network of electrochemical oscillators with the electrodissolution of nickel in sulfuric acid

  • In section Weak Chimera in Modular Networks with Strongly Non-linear Oscillators, new results are presented in a modular network of highly non-linear oscillators coupled through differences in the electrode potentials

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Summary

Introduction

Synchronization of oscillatory chemical reactions is an important dynamical phenomenon with relevance to many physical and biological processes [1]. Studies focused on the dynamics of continuous, stirred tank reactors (CSTRs) where coupling is through active or passive mass transfer, or by electrical means [2,3,4,5,6]. Belousov-Zhabotinsky (BZ) microdroplets [9, 10], beads [11, 12], microwell arrays [13], and nanodroplets [14] provide ways to study synchronization of populations. Electrode arrays can be applied to investigate coupled systems, up to about 100 oscillators [15]. Coupled electrochemical oscillators showed a variety of synchrony patterns with various levels of coherence, including full synchrony [16] and other stable [17] and intermittent [18] cluster states

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