Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation
| Autor: | Zixin Liu, Maoxin Liao, Qimei Xiao, Peiluan Li, Changjin Xu, Shuai Yuan |
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| Rok vydání: | 2021 |
| Předmět: |
Hopf bifurcation
Numerical Analysis Time delays General Computer Science Laplace transform Artificial neural network Computer science Applied Mathematics Order (ring theory) 010103 numerical & computational mathematics 02 engineering and technology Topology Bifurcation diagram 01 natural sciences Stability (probability) Theoretical Computer Science symbols.namesake Modeling and Simulation Stability theory 0202 electrical engineering electronic engineering information engineering symbols 020201 artificial intelligence & image processing 0101 mathematics |
| Zdroj: | Mathematics and Computers in Simulation. 182:471-494 |
| ISSN: | 0378-4754 |
| Popis: | The stability and Hopf bifurcation have important effect on the design of neural networks. By revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we can better apply neural networks to serve humanity. This article is principally concerned with the stability and the emergence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Applying Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential systems, we establish a new sufficient condition to ensure the stability and the emergence of Hopf bifurcation of the addressed fractional-order BAM neural networks with multiple delays. The research indicates that the delay has a vital effect on the stability and the appearance of Hopf bifurcation of fractional-order BAM neural networks. Computer simulations are put into effect to test the effectiveness of the theoretical findings. It is shown that when the sum of time delays crosses some critical values, the stability of networks loses and Hopf bifurcation will happen. |
| Databáze: | OpenAIRE |
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