title: Multiple cusp bifurcations.
abstract: The cusp bifurcation provides one of the simplest routes leading to bistability and hysteresis in neuron dynamics. We show that weakly connected networks of neurons near cusp bifurcations that satisfy a certain adaptation condition have quite interesting and complicated dynamics. First, we prove that any such network can be transformed into a canonical model by an appropriate continuous change of variables. Then we show that the canonical model can operate as a multiple attractor neural network or as a globally asymptotically stable neural network depending on the choice of parameters.
authors.affiliation: Center for Systems Science and Engineering, Arizona State University, Tempe, USA
authors.forename: Eugene M.
authors.initials: EM
authors.lastname: Izhikevich