Synchronization of coupled equations of Morris–Lecar model

The Morris–Lecar equations explicitly modeling the flow of potassium and calcium ions are a two-dimensional description of neuronal spike dynamics. Some research shows that two coupled Morris–Lecar equations can be synchronized, and synchronization takes place regardless of the initial condition if the coupling is strong enough, and even for two equations with different parameter values, coupled asymmetrically. This paper finds a bounded region in phase space that attracts the flow globally and thus contains all points with recurrent behavior. The size of the region can be calculated from the parameter values in the equations and is proportional to external current. And we obtain explicit bounds for this region in terms of the parameter values as a tool for establishing synchronization.