GENERATION OF COLLECTIVE-ACTIVITY STRUCTURES IN A HOMOGENEOUS NEURON-LIKE MEDIUM I: BIFURCATION ANALYSIS OF STATIC STRUCTURES

A general model of the neuron-like medium with a selfconsistent excitation threshold is considered. The necessary and sufficient conditions of stability of static collective-activity structures in this model are found. The structure bifurcations which are possible by additional inertial inhibition introduced by a local excitation threshold are analyzed using a linear approach.