ANTI-PHASE SYNCHRONIZATION OF INHIBITORILY COUPLED NEURONS

Some new insights into the anti-phase synchronization of a network of inhibitorily coupled neurons are presented by means of qualitative analysis and numerical simulation. The network, which satisfies three significant conditions, gives rise to typical anti-phase synchronous solutions. By using the geometric method of dynamical systems, each corresponding reduced network model is analyzed, and a special and important parameter region, called P*-jumping up region, is identified. In terms of some basic properties of the P*-jumping up region, two conditions for the neuron states to enter this region are given. These conditions can be satisfied by adjusting a parameter K that controls the decay speed of the inhibitory coupling. Furthermore, it is concluded that if the parameter K is chosen so as to satisfy the two conditions, then two neurons will achieve anti-phase synchronous oscillation, independent of the initial conditions.