Robust stability of interval bidirectional associative memory neural network with time delays

Area of Science:

• Artificial Intelligence
• Computational Neuroscience
• Control Theory

Background:

• Bidirectional associative memory (BAM) neural networks are crucial for associative learning.
• Signal transmission delays and parameter variations can impact BAM stability.
• Robustness analysis is essential for reliable neural network applications.

Purpose of the Study:

• To develop a novel interval dynamic BAM (IDBAM) model for analyzing parameter deviations and perturbations.
• To investigate the effects of signal transmission delays on BAM stability.
• To derive robust stability criteria for BAM neural networks with time-varying delays and various activation functions.

Main Methods:

• Interval analysis applied to BAM neural networks with signal transmission delays.
• Utilization of multiple Lyapunov functionals combined with the Razumikhin technique.
• Extension of stability analysis to time-varying delay scenarios.

Main Results:

• Sufficient conditions for the existence of a unique equilibrium and robust stability in the IDBAM model were derived.
• Robust stability criteria were established for BAM with perturbations under time-varying delays.
• The analytical approach accommodates diverse activation functions, including piecewise linear and C1-smooth sigmoids.

Conclusions:

• The derived conditions for robust stability are general and easily verifiable.
• The IDBAM model provides a robust framework for analyzing perturbed BAM neural networks.
• The findings hold significant implications for the practical design and application of BAM neural networks.