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Exponential stability of positive neural networks in bidirectional associative memory model with delays
Author(s) -
Hien Le Van,
HaiAn Le Dao
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5725
Subject(s) - mathematics , exponential stability , bidirectional associative memory , initialization , artificial neural network , equilibrium point , fixed point theorem , nonlinear system , stability (learning theory) , fixed point , content addressable memory , differential equation , pure mathematics , mathematical analysis , computer science , physics , quantum mechanics , machine learning , programming language
This paper is concerned with the problem of exponential stability of positive neural networks in bidirectional associative memory (BAM) model with multiple time‐varying delays and nonlinear self‐excitation rates. On the basis of a systematic approach involving extended comparison techniques via differential inequalities, we first prove the positivity of state trajectories initializing from a positive cone called the admissible set of initial conditions. In combination with the use of Brouwer's fixed point theorem and M‐matrix theory, we then derive conditions for the existence and global exponential stability of a unique positive equilibrium of the model. An extension to the case of BAM neural networks with proportional delays is also presented. The effectiveness of the obtained results is illustrated by a numerical example with simulations.