The stability of neural networks is not only the most basic and important problem but also the foundation of some neural network's applications. In this paper, the stability of discrete delayed Hopfield neural networks is mainly investigated by constructing Lyapunov function and taking some inequality techniques into account. The sufficient conditions for discrete delayed Hopfield neural networks converging towards a limit cycle with 4-period are given. Also, some conditions for discrete delayed Hopfield neural networks neither having a stable state nor a limit cycle with 2-period are obtained. The obtained results here extend and improve some previously established results on the stability of discrete Hopfield neural network and the stability of discrete delayed Hopfield neural network in the literature.
[1]
MARunnian,et al.
Dynamic Behavior of Discrete Hopfield Neural Networks with Time-Delay
,
2005
.
[2]
Dong-Liang Lee.
New stability conditions for Hopfield networks in partial simultaneous update mode
,
1999,
IEEE Trans. Neural Networks.
[3]
Long Yang.
Stability conditions for discrete hopfield neural networks with delay
,
2008
.
[4]
Joseph W. Goodman,et al.
A generalized convergence theorem for neural networks
,
1988,
IEEE Trans. Inf. Theory.
[5]
Qiu Shen-sha.
Matrix Criterion for Dynamic Analysis in Discrete Neural Networks with Delay
,
1999
.
[6]
E. Goles.
Antisymmetrical neural networks
,
1986,
Discrete Applied Mathematics.