Journal
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
Volume 47, Issue 15, Pages 3668-3677Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207721.2015.1110641
Keywords
Stability; Hopf bifurcation; time delays; fractional neural networks
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Funding
- National Natural Science Foundation of China [61573096, 61272530]
- Natural Science Foundation of Jiangsu Province of China [BK2012741]
- 333 Engineering Foundation of Jiangsu Province of China [BRA2015286]
- Specialized Research Fund for the Doctoral Program of Higher Education [20130092110017]
- Foundation of Graduate Innovation Programof Jiangsu Province [KYLX15_0107]
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This paper investigates the issue of stability and bifurcation for a delayed fractional neural network with three neurons by applying the sum of time delays as the bifurcation parameter. Based on fractional Laplace transform and the method of stability switches, some explicit conditions for describing the stability interval and emergence of Hopf bifurcation are derived. The analysis indicates that time delay can effectively enhance the stability of fractional neural networks. In addition, it is found that the stability interval can be varied by regulating the fractional order if all the parameters are fixed including time delay. Finally, numerical examples are presented to validate the derived theoretical results.
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