Synchronization of Coupled Time-Delay Neural Networks With Mode-Dependent Average Dwell Time Switching

Area of Science:

• Dynamical Systems and Control Theory
• Computational Neuroscience
• Network Science

Background:

• Existing research on system switching (ADT, Markovian, intermittent coupling) treats them separately.
• Neural networks (NNs) with mixed delays and stochastic perturbations present complex synchronization challenges.
• The need for a unified framework to analyze diverse switching behaviors in dynamic systems.

Purpose of the Study:

• To introduce a novel, unified switching mechanism for analyzing synchronization in complex systems.
• To investigate global exponential synchronization almost surely (GES a.s.) in arrays of neural networks (NNs).
• To address NNs with mixed delays, switching topology, and stochastic perturbations.

Main Methods:

• Development of a general switching mechanism incorporating transition probability (TP) and mode-dependent average dwell time (MDADT).
• Design of a multiple Lyapunov-Krasovskii functional.
• Application of novel analytical techniques to derive synchronization conditions.

Main Results:

• Sufficient conditions derived for achieving GES a.s. in coupled NNs under the proposed unified switching.
• Demonstrated GES a.s. is achievable even with both synchronizing and nonsynchronizing modes.
• Relaxed the restrictive condition on increment coefficients of the Lyapunov-Krasovskii functional at switching instants.

Conclusions:

• The proposed TP-based MDADT switching framework effectively unifies various switching types.
• The developed analytical techniques ensure robust GES a.s. for NNs with complex dynamics.
• The findings offer significant advancements in understanding and controlling synchronization in networked systems.