Spatiotemporal Patterns of Oscillatory Electrochemical Reactions in the Presence of a Low-Pass Filter

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In many electrochemical measurements, the measured signals are often filtered to remove experimental noise, for example, with a low-pass filter (LPF). At the same time, various electrical coupling (potential drop in the electrolyte) and feedback (galvanostatic constraints) effects can generate spatiotemporal patterns. In this contribution, we study the synchronization patterns of electrochemical oscillators induced by feedback in the presence of a low-pass filter. Close to a Hopf bifurcation, without the filter, as expected[1], the synchronization transition took place above a critical coupling strength following a second-order phase (Kuramoto) transition. With LPF, the transition occurred through explosive synchronization, which corresponds to a first-order phase transition and multistability between synchronized and desynchronized states. These experimental results confirm recent theoretical development on the impact of LPF on the synchronization of Stuart-Landau oscillators[2]. Further away from Hopf bifurcation, the LPF can generate patterns with one- and two-cluster states from a desynchronized state. The cluster formation and stability can be understood using a theory that estimates the LPF induced amplitude attenuation and phase shift of the coupling functions in the phase model of the oscillatory process. Our study points to the importance of using filtering in engineering synchronization states of oscillatory electrochemical reactions. Kiss, I.Z., Y. Zhai, and J.L. Hudson, Emerging Coherence in a Population of Chemical Oscillators. Science, 2002. 296(5573): p. 1676.Zou, W., M. Zhan, and J. Kurths, Phase transition to synchronization in generalized Kuramoto model with low-pass filter. Physical Review E, 2019. 100(1): p. 012209.