Uniqueness and stability of periodic bursting solutions

A detailed analysis of so-called square bursting oscillators is given. An interesting feature of these models is that the bursting solution need not be unique or stable for arbitrarily small values of a singular perturbation parameter. This is a global phenomenon due to interactions between a homoclinic orbit and other invariant manifolds. Using geometric singular perturbation methods we characterize the set of parameters for which the bursting solution is uniquely determined and asymptotically stable.