Dynamics and bifurcations of a discrete time neural network with self connection

This paper investigates the dynamical behavior of a discrete-time neural network system from both analytical and numerical points of view. The conditions as well as the critical coefficients for the pitchfork, flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. Using critical coefficients, the bifurcation scenarios were determined for each bifurcation point. By changing one or two parameters, bifurcation curves of fixed points and cycles with periods up to four iterates, were obtained. Numerical analysis validates our analytical results and reveals more complex dynamical behaviors.