Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays

WANG Li-min; SONG Qian-kun; ZHAO Zhen-jiang

doi:10.21656/1000-0887.370221

Volume 38 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(3): 333-346

WANG Li-min, SONG Qian-kun, ZHAO Zhen-jiang. Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays[J]. Applied Mathematics and Mechanics, 2017, 38(3): 333-346. doi: 10.21656/1000-0887.370221

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Global Asymptotic Stability of Memristor-Based Fractional-Order Complex-Valued Neural Networks With Time Delays

doi: 10.21656/1000-0887.370221

¹School of Information Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, P.R.China;²Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, P.R.China;³Department of Mathematics, Huzhou Teachers University, Huzhou, Zhejiang 313000, P.R.China

Funds: The National Natural Science Foundation of China(61273021; 61473332)

Received Date: 2016-07-19
Rev Recd Date: 2016-11-09
Publish Date: 2017-03-15

Abstract

Abstract

The global stability of fractional-order complex-valued neural networks was investigated. For a class of memristor-based fractional-order complex-valued neural networks with time delays, under the concept of the Filippov solution in the sense of Caputo’s fractional derivation, the existence and uniqueness of the equilibrium point were discussed. The comparison principle and the fixed-point theorem were applied to the stability analysis through division of the complex values into the real part and the imaginary part. Some sufficient criteria for the global asymptotic stability of memristor-based fractional-order complex-valued neural networks were derived. Finally, a simulation example shows the effectiveness of the obtained results.
- complex-valued neural network,
- fractional calculus,
- memristor,
- Filippov solution,
- global asymptotic stability

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References(25)

References

[1]	Kilbas A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations [M]. New York: Elsevier Science Inc, 2006.
[2]	Boroomand A, Menhaj M B. Fractional-Order Hopfield Neural Networks [M]//Advances in Neuro-Information Processing. Berlin, Heidelberg: Springer, 2009: 883-890.
[3]	Ahmeda E, Elgazzar A S. On fractional order differential equations model for nonlocal epidemics[J]. Physica A: Statistical Mechanics and Its Applications,2007,379(2): 607-614.
[4]	Diethelm K, Ford N J. Analysis of fractional differential equations[J]. Journal of Mathematical Analysis and Applications,2002,265(2): 229-248.
[5]	YANG Xu-jun, SONG Qian-kun, LIU Yu-rong, et al. Finite-time stability analysis of fractional-order neural networks with delay[J]. Neurocomputing,2015,152: 19-26.
[6]	ZHANG Shuo, YU Yong-guang, WANG Qing. Stability analysis of fractional-order Hopfield neural networks with discontinuous activation functions[J]. Neurocomputing,2016,171: 1075-1084.
[7]	Rakkiyappan R, CAO Jin-de, Velmurugan G. Existence and uniform stability analysis of fractional-order complex-valued neural networks with time delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2015,26: 84-97.
[8]	Chua L. Memristor-the missing circuit element[J]. IEEE Transactions on Circuit Theory,1971,18(5): 507-519.
[9]	HU Jin, WANG Jun. Global uniform asymptotic stability of memristor-based recurrent neural networks with time delays[C]//The 2010 International Joint Conference on Neural Networks.2010: 1-8.
[10]	WU Ai-long, WEN Shi-ping, ZENG Zhi-gang. Synchronization control of a class of memristor-based recurrent neural networks[J]. Information Sciences,2012,183: 106-116.
[11]	BAO Hai-bo, Park Ju H, CAO Jin-de. Adaptive synchronization of fractional-order memristor-based neural networks with time delay[J]. Nonlinear Dynamics,2015,82(3): 1343-1354.
[12]	Velmurugan G, Rakkiyappan R, CAO Jin-de. Finite-time synchronization of fractional-order memristorbased neural networks with time delays[J]. Neural Networks,2016,73: 36-46.
[13]	CHEN Li-ping, WU Ran-chao, CAO Jin-de, et al. Stability and synchronization of memristor-based fractional-order delayed neural networks[J]. Neural Networks,2015,71: 37-44.
[14]	Hirose A. Dynamics of fully complex-valued neural networks[J]. Electronics Letters,1992,28: 1492-1494.
[15]	Nitta T. An analysis of the fundamental structure of complex-valued neurons[J]. Neural Processing Letters,2000,12(3): 239-246.
[16]	HU Jin, WANG Jun. Global stability of complex-valued recurrent neural networks with time-delays[J]. IEEE Transactions on Neural Networks and Learning Systems,2012,23(6): 853-865.
[17]	ZHOU Bo, SONG Qian-kun. Boundedness and complete stability of complex-valued neural networks with time delay[J]. IEEE Transactions on Neural Networks and Learning Systems,2013,24(8): 1227-1238.
[18]	ZHANG Zi-ye, LIN Chong, CHEN Bing. Global stability criterion for delayed complex-valued recurrent neural networks[J]. IEEE Transactions on Neural Networks and Learning Systems,2014,25: 1704-1708.
[19]	SONG Qian-kun, ZHAO Zhen-jiang. Stability criterion of complex-valued neural networks with both leakage delay and time-varying delays on time scales[J]. Neurocomputing,2016,171: 179-184.
[20]	HU Shou-chuan. Differential equations with discontinuous right-hand sides[J]. Journal of Mathematical Analysis and Applications, 1991,154(2): 377-390.
[21]	ZHANG Guo-dong, SHEN Yi, SUN Jun-wei. Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays[J]. Nonlinear Analysis:Hybrid Systems,2012,97: 149-154.
[22]	ZHANG Shuo, YU Yong-guang, WANG Hu. Mittag-Leffler stability of fractional-order Hopfield neural networks[J]. Nonlinear Analysis: Hybrid Systems, 2015,16: 104-121.
[23]	WANG Hu, YU Yong-guang, WEN Guo-guang, et al. Global stability analysis of fractional-order Hopfield neural networks with time delay[J]. Neurocomputing,2015,154: 15-23.
[24]	DENG Wei-hua, LI Chang-pin, LU Jin-hu, et al. Stability analysis of linear fractional differential system with multiple time delays[J]. Nonlinear Dynamics,2007,48(4): 409-416.
[25]	CHEN Jie-jie, ZENG Zhi-gang, JIANG Ping. Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks[J]. Neural Networks,2014,51: 1-8.