Synchronization of electrochemical oscillators of S-NDR type

Electrochemical oscillators are classified as truly potentiostatic or Negative Differential Resistance (NDR) type considering, respectively, the nonessential or essential role of double-layer potential on the dynamics. NDR type oscillators are further grouped into N-NDR and S-NDR type systems where N and S refer to the characteristic shape of the polarization curve. Here, we report on the effect of global coupling on the dynamics of interacting electrochemical oscillators of S-NDR type where the electrode potential acts as an essential negative feedback variable. The Lee–Jorné scheme has been applied to model Zn electrodeposition on two or an array of 128 globally coupled nonidentical electrodes. The strength of global coupling between the electrodes can be systematically varied by changing collective and individual resistors in the circuit. Several different scenarios for synchronization and partial synchronization have been observed and analyzed. The collective dynamics is characterized by an order parameter, the average phase shift between the oscillators, and phase portraits based on Hilbert transform. The effect of changing the double-layer capacitance on the dynamics is also explored.