Direct and Retrograde Wave Propagation in Unidirectionally Coupled Wilson-Cowan Oscillators

Some biological systems exhibit both direct and retrograde propagating signal waves despite unidirectional coupling. To explain this phenomenon, we study a chain of unidirectionally coupled Wilson-Cowan oscillators. Surprisingly, we find that changes in the homogeneous global input to the chain suffice to reverse the wave propagation direction. To obtain insights, we analyze the frequencies and bifurcations of the limit cycle solutions of the chain as a function of the global input. Specifically, we determine that the directionality of wave propagation is controlled by differences in the intrinsic frequencies of oscillators caused by the differential proximity of the oscillators to a homoclinic bifurcation.