Global dissipativity analysis for delayed quaternion-valued neural networks.

Area of Science:

• Complex Systems Analysis
• Neural Network Theory
• Control Theory

Background:

• Quaternion-valued neural networks (QVNNs) offer advanced computational capabilities.
• Analyzing stability and convergence in systems with time-varying delays remains a significant challenge.
• Dissipativity is a crucial concept for understanding system stability and boundedness.

Purpose of the Study:

• To investigate the global dissipativity of quaternion-valued neural networks (QVNNs) with time-varying delays.
• To develop new algebraic conditions for ensuring global and exponential dissipativity.
• To determine positive invariant, globally attractive, and globally exponentially attractive sets for QVNNs.

Main Methods:

• Lyapunov theory application.
• Development of novel analytic techniques.
• Analysis of QVNNs as a single, non-decomposed entity.

Main Results:

• Derivation of several algebraic conditions for global dissipativity and globally exponential dissipativity.
• Identification of positive invariant sets, globally attractive sets, and globally exponentially attractive sets.
• Validation of the derived conditions through two simulation examples.

Conclusions:

• The proposed methods effectively ensure global dissipativity for QVNNs with time-varying delays.
• The findings contribute to a deeper understanding of stability and convergence properties in complex neural network architectures.
• The established conditions and identified sets provide valuable tools for designing and analyzing robust QVNNs.