Transition of phase locking modes in a minimal neuronal network

We investigate the dynamics of phase locking in a minimal neuronal network, which is composed of two Morris-Lecar neurons that are coupled by inhibitory and excitatory synapses as the synaptic strength is varied. Studies show that the synaptic strength can induce various phase locking modes and complex chaotic behaviors. In particular, two coupled neurons may display the complicated transitions between various periodic phase locking modes and chaotic states. It is shown that those transitions are accompanied by the tangent bifurcation, where the different phase locking modes can be related to the appearance of periodic windows. Furthermore, we explore the dynamical mechanism of the phase locking modes by means of the phase plane analysis. Interestingly, we have found two types of 2:1 phase locking modes, which are characterized by a thin tadpole tail and a fat tadpole tail, respectively. And then, two types of 2:1 phase locking modes are analyzed in detail for understanding their dynamical mechanism. The obtained results can be helpful to explore realistic neuronal activities.