Stability Analysis of Discrete Hopfield Neural Networks with the Nonnegative Definite Monotone Increasing Weight Function Matrix | Zendy

Jun Li | Zendy; Diao Yong-feng | Zendy; Mingdong Li | Zendy; Yin Xing | Zendy

Open Access

Stability Analysis of Discrete Hopfield Neural Networks with the Nonnegative Definite Monotone Increasing Weight Function Matrix

Author(s) -

Jun Li,

Diao Yong-feng,

Mingdong Li,

Yin Xing

Publication year - 2009

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2009/673548

Subject(s) - hopfield network , mathematics , artificial neural network , matrix (chemical analysis) , lyapunov function , weight function , positive definite matrix , function (biology) , nonnegative matrix , monotone polygon , activation function , stability (learning theory) , symmetric matrix , computer science , mathematical analysis , artificial intelligence , eigenvalues and eigenvectors , nonlinear system , materials science , physics , geometry , quantum mechanics , evolutionary biology , machine learning , composite material , biology

The original Hopfield neural networks model is adapted so that the weights of the resulting network are time varying. In this paper, the Discrete Hopfield neural networks with weight function matrix (DHNNWFM) the weight changes with time, are considered, and the stability of DHNNWFM is analyzed. Combined with the Lyapunov function, we obtain some important results that if weight function matrix (WFM) is weakly (or strongly) nonnegative definite function matrix, the DHNNWFM will converge to a stable state in serial (or parallel) model, and if WFM consisted of strongly nonnegative definite function matrix and column (or row) diagonally dominant function matrix, DHNNWFM will converge to a stable state in parallel model

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