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A τ ‐type stability criteria in division regions for multitime‐scale networks with delays
Author(s) -
Huang Zhenkun
Publication year - 2011
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.1525
Subject(s) - multistability , hebbian theory , division (mathematics) , stability (learning theory) , mathematics , artificial neural network , convergence (economics) , scale (ratio) , type (biology) , term (time) , topology (electrical circuits) , computer science , artificial intelligence , nonlinear system , machine learning , combinatorics , geography , ecology , physics , arithmetic , quantum mechanics , economics , biology , economic growth , cartography
This paper is concerned with new results onA τ ‐type stability criteria in division regions for competitive neural networks with different time scales. Under the decomposition of state space, both the neural activity levels (the short‐term memory) and the synaptic modifications (the long‐term memory), are taken into account in constructing division regions that allow the coexistence of equilibrium points. Meanwhile, novel delay‐dependent multistability and monostability criteria are established in division regions that depend on divisions in index set of neurons and boundedness of unsupervised synaptic variables. The attained results show the effects of self‐interactions of neurons and Hebbian learning behavior on the multistable convergence of the networks. Finally, numerical simulations will illustrate multistable neuron activity and synaptic dynamics of multitime‐scale competitive networks. Copyright © 2011 John Wiley & Sons, Ltd.