A Lyapunov-Based Analysis on the Almost Periodicity of Impulsive Conformable Reaction-Diffusion Neural Networks with...

Area of Science:

• Dynamical Systems and Control Theory
• Computational Neuroscience
• Mathematical Physics

Background:

• Reaction-diffusion neural networks are crucial for modeling complex spatio-temporal phenomena.
• Distributed delays and conformable derivatives introduce sophisticated dynamics.
• Impulsive perturbations represent sudden external influences.

Purpose of the Study:

• To investigate the qualitative behavior, specifically almost periodicity, of a reaction-diffusion neural network model.
• To analyze the global conformable exponential stability of the proposed network.
• To develop new analytical criteria for these dynamic properties.

Main Methods:

• A Lyapunov-based approach was employed for stability analysis.
• A novel Lyapunov-type function was constructed.
• Criteria for existence, uniqueness, and stability were mathematically derived.

Main Results:

• Sufficient conditions for the existence and uniqueness of an almost periodic state were established.
• The global conformable exponential stability of the network was analyzed.
• The findings extend existing results in the study of conformable models.

Conclusions:

• The research provides a robust framework for analyzing the dynamics of impulsive reaction-diffusion neural networks with conformable derivatives.
• The established criteria contribute to a deeper understanding of almost periodicity and stability in complex neural models.
• The study offers valuable insights for the design and control of such systems.