Homogeneous modes of work of the neurone networks-II. Periodic solutions and stability of steady states

The spatial homogeneous modes of operation of a neuronal network are considered. The existence is demonstrated of modes of three different types characterized by constancy in time of the particular parameters. Investigation of the modes close to stationary yielded a characteristic equation the roots of which permit solution of the problem of the stability of the corresponding steady state. In the general form the instability of modes with anomalous period of operation of the cell is demonstrated. It is shown that the problem of stability of modes with a normal period of operation of the cell is solved in a way differing with the form of the synaptic current and the distribution function of the links between the cells.