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Published on: March 2, 2015
Complete stability in multistable delayed neural networks
Chang-Yuan Cheng1, Chih-Wen Shih
1Department of Applied Mathematics, National Pingtung University of Education, Pingtung, Taiwan 900, ROC. cycheng@mail.npue.edu.tw
Neural Computation
|October 22, 2008
Summary
This study proves complete stability for multistable delayed neural networks. All network solutions converge to a single equilibrium, confirming previous findings on equilibria and invariant sets.
Area of Science:
- Computational neuroscience
- Dynamical systems theory
- Artificial neural networks
Background:
- Multistable delayed neural networks exhibit complex dynamics.
- Previous formulations have established the existence of multiple equilibria and invariant sets.
Purpose of the Study:
- To investigate the complete stability of multistable delayed neural networks.
- To develop a new formulation for analyzing componentwise dynamical properties.
- To confirm the convergence of all network solutions to a single equilibrium.
Main Methods:
- A novel formulation for multistable networks was developed.
- Componentwise dynamical properties were derived.
- An iteration argument was constructed to prove convergence.
Main Results:
- The new formulation supports the existence of 3n equilibria and 2n positively invariant sets for an n-neuron system.
- It was proven that every solution converges to a single equilibrium over time.
- The theoretical findings were validated through a numerical illustration.
Conclusions:
- The study establishes complete stability for multistable delayed neural networks.
- The developed formulation provides a robust framework for analyzing these networks.
- The results confirm and extend previous theoretical understandings of network behavior.
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