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We investigate dynamics and bifurcations in a mathematical model thatcaptures electrochemical experiments on arrays of microelectrodes. Inisolation, each individual microelectrode is described by a one-dimensionalunit with a bistable current-potential response. When an array of suchelectrodes is coupled by controlling the total electric current, the commonelectric potential of all electrodes oscillates in some interval of thecurrent. These coupling-induced collective oscillations of bistableone-dimensional units are captured by the model. Moreover, any equilibrium iscontained in a cluster subspace, where the electrodes take at most threedistinct states. We systematically analyze the dynamics and bifurcations of themodel equations: We consider the dynamics on cluster subspaces of successivelyincreasing dimension and analyze the bifurcations occurring therein. Mostimportantly, the system exhibits an equivariant transcritical bifurcation oflimit cycles. From this bifurcation, several limit cycles branch, one of whichis stable for arbitrarily many bistable units.

Bifurcations of Clusters and Collective Oscillations in Networks of Bistable Units