Stability switches and bifurcation analysis of a neural network with continuously delay

A continuously delayed neural network with strong kernel is investigated. We found that a switch from stability to instability may occur for certain range of system parameters and must then be followed by a switch back to stability. We also investigate bifurcation phenomena of this model. Using the mean time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs, i.e., a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter passes through a critical value. Stability criteria for the bifurcating periodic solutions are obtained. Some computer simulations illustrate correctness of the results.