Analysis for Dynamics of Discrete Time Hopfield Network

Hopfield network model with discrete time is a nonlinear dynamic system With introduced new energy functions for the state variables of network in this paper, the condition under which the state energy of network will decrease monotonously can be derived by the subgradient property of convex function For Hopfield network with the symmetrical synapse connections among neurons and the no decreasing （not necessary to increase strictly） activation function of each neuron, it will be convergent asymptotically in parallel mode if the gain of neuron activation function is greater than eigenvalue of minimization, and so is it in asynchronous mode if the sum of the gain of neuron activation function and the synapse weight of neuron self feedback connection is greater than zero By using of subgradient property of convex function, it will converge to a limit cycle with period less than 2 in parallel mode for discrete time Hopfield network model with the symmetrical synapse connections among neurons and the no decreasing （not necessary to increase strictly） activation function of each neuron