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Stability of Delayed Reaction-Diffusion Neural-Network Models With Hybrid Impulses via Vector Lyapunov Function
This study analyzes the stability of delayed reaction-diffusion neural networks with hybrid impulses. The findings demonstrate that network stability can be maintained even with these impulses, enabling successful neural network synchronization.
Area of Science:
- Computational Neuroscience
- Control Theory
- Dynamical Systems
Background:
- Delayed reaction-diffusion neural networks are crucial in various applications.
- Impulsive effects in neural networks present challenges for stability analysis.
- Existing methods often require strict conditions on impulse thresholds.
Purpose of the Study:
- To investigate the stability of delayed reaction-diffusion neural networks with hybrid impulses.
- To develop new theoretical frameworks for analyzing such systems.
- To demonstrate the feasibility of achieving synchronization in these networks.
Main Methods:
- Utilizing a vector Lyapunov function approach.
- Applying properties of vector Halanay-type inequalities.
- Establishing Krasovskii-type theorems for exponential stability.
Main Results:
- Sufficient conditions for exponential stability are derived.
- The common threshold requirement for impulses is removed.
- Stability is shown to be achievable with hybrid impulses.
- Synchronization of neural networks is demonstrated via an impulsive controller.
Conclusions:
- The proposed methods effectively analyze the stability of delayed reaction-diffusion neural networks with hybrid impulses.
- The results allow for more flexible impulse design in neural network control.
- The theoretical findings are validated by numerical examples and an image encryption application.
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