Multistability of delayed fractional-order competitive neural networks

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Fractional Calculus

Background:

• Fractional-order competitive neural networks (FCNNs) exhibit complex dynamics.
• Time-varying delays introduce significant challenges in analyzing network stability.
• Understanding multistability is crucial for advanced neural network applications.

Purpose of the Study:

• To investigate the multistability of fractional-order competitive neural networks (FCNNs) with time-varying delays.
• To develop sufficient conditions for O(t^-α)-stability, an extension of Mittag-Leffler stability.
• To estimate the attraction basins of stable equilibrium points in FCNNs.

Main Methods:

• Division of state space to identify equilibrium points (EPs).
• Development of novel criteria for ascertaining multiple O(t^-α)-stability.
• Estimation of attraction basin sizes for stable EPs.

Main Results:

• Sufficient conditions and criteria for multiple O(t^-α)-stability of delayed FCNNs are established.
• The proposed criteria extend and improve upon existing results in the field.
• Attraction basins of stable EPs were found to potentially exceed the divided state space subsets.

Conclusions:

• The study provides a robust framework for analyzing multistability in FCNNs.
• The developed criteria enhance the understanding of stability properties in fractional-order systems.
• Simulation examples validate the theoretical findings and demonstrate practical applicability.