Heteroclinic Orbits and Chaos in A Ring of Three Unidirectionally Coupled Nonmonotonic Neurons

Bifurcations and chaos in a ring of three unidirectionally coupled nonmonotonic neurons are examined. The Hopf bifurcations of steady states generated through saddlenode bifurcations occur, which are accompanied with homoclinic bifurcations. Heteroclinic orbits connecting these steady states are generated and Shil'nikov's chaos emerges. It is indicated that the second bump in the nonmonotonic output function of neurons is intrinsic for the emergence of homoclinic and heteroclinic orbits as well as chaos.