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Published on: July 21, 2021
Global synchronization in an array of delayed neural networks with hybrid coupling
Jinde Cao1, Guanrong Chen, Ping Li
1Department of Mathematics, Southeast University, Nanjing, China. jdcao@seu.edu.cn
Summary
This study introduces a general array model for coupled delayed neural networks with hybrid coupling. It establishes conditions for global exponential synchronization using Lyapunov functionals and Kronecker products, validated with chaotic neural networks.
Area of Science:
- Neuroscience
- Systems Theory
- Control Theory
Background:
- Coupled delayed neural networks are crucial for complex system modeling.
- Hybrid coupling (constant, discrete, distributed delays) presents unique synchronization challenges.
- Achieving global exponential synchronization is key for network stability and performance.
Purpose of the Study:
- To propose and analyze a general array model for coupled delayed neural networks with hybrid coupling.
- To develop sufficient conditions for achieving global exponential synchronization.
- To demonstrate the model's effectiveness using a chaotic cellular neural network example.
Main Methods:
- Lyapunov functional method for stability analysis.
- Kronecker product properties for matrix manipulations.
- Design of coupling, inner linking, and free matrices.
- Linear Matrix Inequalities (LMIs) for computational ease.
Main Results:
- Established several sufficient conditions for global exponential synchronization.
- Conditions are expressed in an easily computable LMI format.
- Demonstrated effectiveness and advantages through a chaotic cellular neural network simulation.
Conclusions:
- The proposed array model effectively facilitates global exponential synchronization in coupled delayed neural networks.
- The developed conditions, based on LMIs, offer a computationally efficient approach to synchronization.
- The study provides a robust theoretical framework with practical implications for neural network design.
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