New generalized Halanay inequalities and relative applications to neural networks with variable delays

The asymptotic behavior of solutions for a new class of generalized Halanay inequalities is studied via the fixed point method. This research provides a new approach to the study of the stability of Halanay inequality. To make the application of fixed point method in stability research more flexible...

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Bibliographic Details
Published in:Boundary value problems 2023-09, Vol.2023 (1), p.95-16, Article 95
Main Authors: Wang, Chunsheng, Chen, Han, Lin, Runpeng, Sheng, Ying, Jiao, Feng
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Asymptotic properties
Asymptotic stability
Boundary value problems
Difference and Functional Equations
Dynamical systems
Fixed point method
Fixed points (mathematics)
Generalized Halanay inequalities
Inequalities
Mathematics
Mathematics and Statistics
Neural network
Neural networks
Ordinary Differential Equations
Partial Differential Equations
Stability
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Summary:The asymptotic behavior of solutions for a new class of generalized Halanay inequalities is studied via the fixed point method. This research provides a new approach to the study of the stability of Halanay inequality. To make the application of fixed point method in stability research more flexible and feasible, we introduce corresponding functions to construct an operator according to different characteristics of coefficients. The results obtained in this paper are applied to the stability study of a neural network system, which has high value in application. Moreover, three examples and simulations are given to illustrate the results. The conclusions in this paper greatly improve and generalize the relative results in the current literature.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-023-01773-8