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

• Pinning of rotating waves in a ring of asymmetric sigmoidal neurons is studied.
• A ring has asymmetric bidirectional coupling and self-coupling.
• There are multiple pinned states with unsaturated neurons at wave fronts.
• Pinning conditions depend on whether coupling is excitatory or inhibitory.

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.