Journal
CHAOS SOLITONS & FRACTALS
Volume 164, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2022.112676
Keywords
Nonlinear delay differential equation; Infinite delay; Asymptotic stability; Exponential stability; Bidirectional associative memory neural networks
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Funding
- Portuguese Funds through FCT (Fundacao para a Ciencia e a Tecnologia) [UIDB/00013/2020, UIDP/00013/2020]
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This paper provides sufficient conditions for the global asymptotic stability of a general n-dimensional nonautonomous and nonlinear differential equation with infinite delay. The main stability criterion depends on the delay size on the linear part and the dominance of linear terms over nonlinear terms. The obtained theoretical stability results are applied to answer open problems and generalize a bidirectional associative memory neural network model with delays. A numerical example is given to illustrate the novelty of the results.
For a general n-dimensional nonautonomous and nonlinear differential equation with infinite delay, we give sufficient conditions for its global asymptotic stability. The main stability criterion depends on the size of the delay on the linear part and the dominance of the linear terms over the nonlinear terms. We apply our main result to answer several open problems left by Berezansky et al. (2014). Using the obtained theoretical stability results, we get sufficient conditions for both the global asymptotic and global exponential stability of a bidirectional associative memory neural network model with delays which generalizes models recently studied. Finally, a numerical example is given to illustrate the novelty of our results.
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