Dynamic analysis of a class of fractional-order neural networks with delay

Neurocomputing

Volumn 111, Issue , 2013, Pages 190-194

  Chen, Liping ^a   Chai, Yi ^a   Wu, Ranchao ^b   Ma, Tiedong ^a   Zhai, Houzhen ^a  

^a CHONGQING UNIVERSITY   (China)

^b ANHUI UNIVERSITY   (China)

Author keywords

Delay; Fractional order neural networks; Uniform stability

Indexed keywords

DELAY; EQUILIBRIUM POINT; FRACTIONAL ORDER; NUMERICAL EXAMPLE; SUFFICIENT CONDITIONS; UNIFORM STABILITY;

COMPUTER APPLICATIONS;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER; CONTROLLED STUDY; FRACTIONAL ORDER NEURAL NETWORK; MATHEMATICAL PHENOMENA; PRIORITY JOURNAL; TIME; TIME DELAY; UNIFORM STABILITY; VALIDITY;

EID: 84876741903     PISSN: 09252312     EISSN: 18728286     Source Type: Journal    
DOI: 10.1016/j.neucom.2012.11.034     Document Type: Article

References (23)

1. Podlubny I. Fractional Differential Equations 1999, Academic Press, San Diego.
2. Hilfer R. Applications of Fractional Calculus in Physics 2000, World Scientific York, Singapore.
3. Özalp N., Demirci E. A fractional order SEIR model with vertical transmission. Math. Comput. Modell. 2011, 54(1-2):1-6.
4. Laskin N. Fractional market dynamics. Physica A 2000, 287(3-4):482-492.
5. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Application of Fractional Differential Equations 2006, Elsevier, New York.
6. Ahmeda E., Elgazzar A.S. On fractional order differential equations model for nonlocal epidemics. Physica A 2007, 379:607-614.
7. Lundstrom B., Higgs M., Spain W., Fairhall A. Fractional differentiation by neocortical pyramidal neurons. Nat. Neurosci. 2008, 11:1335-1342.
8. Anastasio T. The fractional-order dynamics of brainstem vestibulo-oculomotor neurons. Biol. Cybern. 1994, 72:69-79.
9. Anastassiou G. Fractional neural network approximation. Comput. Math. Appl. 2012, 64:1655-1676.
10. Kaslika E., Sivasundaram S. Nonlinear dynamics and chaos in fractional-order neural networks. Neural Networks 2012, 32:245-256.
11. Arena P., Fortuna L., Porto D. Chaotic behavior in noninteger-order cellular neural networks. Phys. Rev. E 2000, 61:776-781.
12. A. Boroomand, M. Menhaj, Fractional-order Hopfield neural networks, in: Lecture Notes in Computer Science, vol. 5506, 2009, pp. 883-890.
13. Huang X., Zhao Z., Wang Z., Lia Y.X. Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing 2012, 94:13-21.
14. Yu J., Hu C., Jiang H. α-Stability and α-synchronization for fractional-order neural networks. Neural Networks 2012, 35:82-87.
15. S. Zhou, P. Hu, H. Li, Chaotic synchronization of a fractional neuron network system with time-varying delays, in: 2009 International Conference on Communications, Circuits and Systems, 2009, pp. 863-867.
16. Zhou S., Li H., Zhu Z. Chaos control and synchronization in a fractional neuron network system. Chaos Solitons Fractals 2008, 36:973-984.
17. H. Zhu, S. Zhou, W. Zhang, Chaos and synchronization of time-delayed fractional neuron network system, in: Proceedings of the Ninth International Conference for Young Computer Scientists, 2008, pp. 2937-2941.
18. Zheng C., Zhang H., Wang Z. Novel delay-dependent criteria for global robust exponential stability of delayed cellular neural networks with norm-bounded uncertainties. Neurocomputing 2009, 72:1744-1754.
19. Huang Y., Zhang H., Wang Z. Dynamical stability analysis of multiple equilibrium points in time-varying delayed recurrent neural networks with discontinuous activation functions. Neurocomputing 2012, 91:21-28.
20. Zhang H., Dong M., Wang Y., Sun N. Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping. Neurocomputing 2010, 73:2689-2695.
21. Li C., Feng G. Delay-interval-dependent stability of recurrent neural networks with time-varying delay. Neurocomputing 2009, 72:1179-1183.
22. Wu S., Li C., Liao X., Duan S. Exponential stability of impulsive discrete systems with time delay and applications in stochastic neural networks. a Razumikhin approach. Neurocomputing 2012, 82:29-36.
23. Li C.P., Deng W.H. Remarks on fractional derivatives. Appl. Math. Comput. 2007, 187:777-784.