The McKean model with synaptic conductance and gated thresholds is studied.The existence and stability of the equilibrium point of the system are given.The persistence and non-smooth fold bifurcation of the boundary equilibrium point of the system are theoretically analyzed.And by introducing the generalized Jacobi matrix near the switching manifold,the parameter conditions for the occurrence of discontinuous Hopf bifurcation in the system are theoretically deduced,and then the existence of the cross-bounda...
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