Lag H_∞ synchronization in coupled reaction-diffusion neural networks with multiple state or derivative couplings

Area of Science:

• Computational Neuroscience
• Control Theory
• Dynamical Systems

Background:

• Reaction-diffusion neural networks (RDNNs) are crucial for modeling complex spatio-temporal dynamics.
• Synchronization is a key phenomenon in neural systems, with lag synchronization being particularly relevant.
• Parameter uncertainties in RDNNs pose significant challenges for achieving reliable synchronization.

Purpose of the Study:

• To investigate lag H_∞ synchronization in two types of coupled RDNNs with parameter uncertainties.
• To develop robust control strategies for achieving guaranteed lag H_∞ synchronization.
• To establish novel criteria for lag H_∞ synchronization in these complex neural network models.

Main Methods:

• Design of novel reaction-diffusion neural network models with multiple state or derivative couplings and parameter uncertainties.
• Development of state feedback controllers utilizing Lyapunov functional and inequality techniques.
• Application of adaptive control strategies to address synchronization issues under uncertainty.

Main Results:

• Formulation of several criteria for achieving lag H_∞ synchronization in the proposed RDNNs.
• Demonstration of the effectiveness of designed state feedback and adaptive control strategies.
• Validation of the theoretical findings through two illustrative numerical examples.

Conclusions:

• The proposed methods and criteria effectively achieve lag H_∞ synchronization in reaction-diffusion neural networks with parameter uncertainties.
• The study contributes novel control techniques for robust synchronization in complex dynamical systems.
• The findings have implications for understanding and controlling spatio-temporal patterns in neural systems.