Synchronization of impulsive coupled complex-valued neural networks with delay: The matrix measure method

Area of Science:

• Complex Systems
• Computational Neuroscience
• Nonlinear Dynamics

Background:

• Complex-valued neural networks (CVNNs) are crucial for modeling complex phenomena.
• Synchronization in neural networks is vital for information processing.
• Impulsive coupling and delays introduce significant challenges in analyzing CVNNs.

Purpose of the Study:

• To investigate the exponential synchronization of impulsive coupled delayed CVNNs.
• To develop a novel analytical approach bypassing traditional Lyapunov function construction.
• To remove common restrictions on activation functions and impulsive interval bounds.

Main Methods:

• Utilizing matrix measure and extended Halanay inequality for analysis.
• Developing a new approach independent of Lyapunov functions.
• Applying the average impulsive interval method to relax constraints on impulse intervals.

Main Results:

• Sufficient criteria for achieving exponential synchronization in addressed CVNNs are derived.
• The proposed method successfully removes the restriction on the real and imaginary parts of activation functions.
• The requirement on the upper bound of impulsive intervals is eliminated.

Conclusions:

• The presented theoretical results are validated through numerical examples.
• The approach demonstrates effectiveness for large-scale CVNNs with impulsive coupling.
• This work contributes a more generalized framework for analyzing synchronization in complex dynamical systems.