Synchronization of chaotic neural networks with time delay via distributed delayed impulsive control

Area of Science:

• Computational Neuroscience
• Control Theory
• Dynamical Systems

Background:

• Chaotic neural networks are complex systems exhibiting sensitive dependence on initial conditions.
• Time delays in neural networks can lead to intricate dynamics and synchronization challenges.
• Impulsive control strategies offer effective methods for stabilizing or synchronizing dynamical systems.

Purpose of the Study:

• To investigate the impulsive synchronization of chaotic neural networks with time delays.
• To develop a novel impulsive delayed inequality that accounts for distributed delayed impulses.
• To design a distributed delayed impulsive controller for achieving exponential synchronization.

Main Methods:

• Proposal of a novel impulsive delayed inequality.
• Development of a distributed delayed impulsive controller.
• Utilizing numerical simulations to demonstrate synchronization effectiveness.

Main Results:

• The proposed impulsive delayed inequality fully considers the control effect of distributed delayed impulses.
• The designed controller achieves exponential synchronization of chaotic neural networks with time delays.
• Numerical examples confirm the theoretical findings and controller efficacy.

Conclusions:

• The novel approach effectively addresses impulsive synchronization in chaotic neural networks with time delays.
• The proposed controller provides a robust method for achieving exponential synchronization.
• This work contributes to the understanding and control of complex neural network dynamics.