Dynamics of a continuous-valued discrete-time Hopfield neural network with synaptic depression

Authors:
Zhijie Wang;Hong Fan
Affiliations:
College of Information Science and Technology, Donghua University, Shanghai 201620, China;Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan
Venue:
Neurocomputing
Year:
2007

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Abstract

A continuous-valued discrete-time Hopfield neural network with synaptic depression (CDHSD) is constructed. We prove that the fixed point of CDHSD is the same as that of a network without synaptic depression and with an activation function determined by the parameters of the synaptic depression. We analyze the stability of the equilibrium, and then give a sufficient condition for the existence of a unique equilibrium of CDHSD. Numerical analysis shows that the attractor of CDHSD might be an equilibrium, a periodic orbit or a nonperiodic orbit depending on its parameter values and initial conditions. A weak external input of the network contributes to the genesis of nonperiodic dynamics of the network. If the value of parameter @?, which is the steepness parameter of the activation function f(x)=1/(1+exp(-x/@?)), is large enough or small enough, nonperiodic dynamics of CDHSD does not appear. It is also shown that nonperiodic dynamics is likely to emerge with intermediate strength of synaptic depression.