Effects of asymmetry in an output function on the pinning of rotating waves in a ring neural oscillator with asymmetric bidirectional coupling and self-coupling

Abstract

Effects of asymmetry in a sigmoidal output function of neurons on rotating waves in a ring of neurons with asymmetric bidirectional coupling and self-coupling were studied. Propagation of wave fronts in rotating waves failed, i.e., the pinning of rotating waves occurred not only when self-coupling was excitatory but also when self-coupling was inhibitory, in which there were unsaturated neurons at wave fronts. Conditions for the pinning of wave fronts were derived by using a piecewise linear output function. The pinning conditions depended on whether bidirectional coupling was excitatory or inhibitory in the presence of asymmetry in an output function.