Paper Info
Title
Dynamics of a continuous-valued discrete-time Hopfield neural network with synaptic depression
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.
Year
DOI
Venue
2007
10.1016/j.neucom.2007.01.004
Neurocomputing
Keywords
Field
DocType
parameter value,nonperiodic orbit,synaptic depression,activation function,steepness parameter,small enough,periodic orbit,unique equilibrium,nonperiodic dynamic,continuous-valued discrete-time hopfield neural,numerical analysis,neural networks,neural network,initial condition,equilibrium,fixed point,discrete time
Attractor,Control theory,Artificial intelligence,Fixed point,Artificial neural network,Statistical physics,Orbit,Pattern recognition,Activation function,Discrete time and continuous time,Numerical analysis,Periodic orbits,Mathematics
Journal
Volume
Issue
ISSN
71
1-3
Neurocomputing
Citations 
PageRank 
References 
2
0.41
22
Authors
2
Name
Order
Citations
PageRank
Zhijie Wang18911.14
Hong Fan220.41