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Multistability and Stabilization of Fractional-Order Competitive Neural Networks With Unbounded Time-Varying Delays
IEEE Transactions on Neural Networks and Learning Systems
|February 25, 2021
Summary
This study explores multistability and stabilization in fractional-order competitive neural networks (FOCNNs) with time-varying delays. New criteria ensure multiple equilibrium points and stability, improving upon existing fractional-order neural network research.
Area of Science:
- Computational Neuroscience
- Dynamical Systems Theory
- Control Theory
Background:
- Fractional-order competitive neural networks (FOCNNs) are crucial for modeling complex systems.
- Unbounded time-varying delays introduce significant challenges in analyzing network stability.
- Multistability and stabilization are key properties for reliable FOCNN applications.
Purpose of the Study:
- To investigate the multistability and stabilization of FOCNNs with unbounded time-varying delays.
- To establish sufficient conditions for the coexistence of multiple equilibrium points (EPs).
- To derive criteria for multiple μ-stability and controller-based stabilization.
Main Methods:
- Monotone operator theory to analyze equilibrium point coexistence.
- Analytical methods to derive multiple μ-stability criteria.
- Controller design for network stabilization in the presence of uncertainty.
Main Results:
- Sufficient conditions for the coexistence of multiple EPs in FOCNNs with concave-convex activation functions.
- Derived multiple μ-stability criteria for delayed FOCNNs.
- Established criteria for the stabilization of uncertain FOCNNs via controller design.
- Demonstrated that results encompass inverse-power and Mittag-Leffler stability.
Conclusions:
- The study provides novel and improved results for fractional-order neural networks.
- The findings enhance the understanding and control of complex dynamical systems modeled by FOCNNs.
- Numerical examples validate the effectiveness of the proposed theoretical results.
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