Influence of multiple time delays on bifurcation of fractional-order neural networks. (English) Zbl 1428.34111
Summary: In this article, on the basis of predecessors works, we will propose a new fractional-order neural network model with multiple delays. Letting two different delays be bifurcation parameters and analyzing the corresponding characteristic equations of considered model, we will establish a set of new sufficient criteria to guarantee the stability and the appearance of Hopf bifurcation of fractional-order network model with multiple delays. The impact of two different delays on the stability behavior and the emergence of Hopf bifurcation of involved network model is revealed. The influence of the fractional order on the stability and Hopf bifurcation of involved model is also displayed. To check the correctness of analytical results, we perform programmer simulations with software. A conclusion is drawn in the end. The analysis results in this article are innovative and have important theoretical significance in designing neural networks.
MSC:
| 34K20 | Stability theory of functional-differential equations |
| 34K37 | Functional-differential equations with fractional derivatives |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 34K18 | Bifurcation theory of functional-differential equations |
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