基于忆阻的时滞神经网络的全局稳定性

胡进; 宋乾坤

doi:10.3879/j.issn.1000-0887.2013.07.007

基于忆阻的时滞神经网络的全局稳定性

doi: 10.3879/j.issn.1000-0887.2013.07.007

胡进,
宋乾坤

重庆交通大学理学院, 重庆 400074

基金项目: 国家自然科学基金资助项目(61273021);重庆市自然科学基金重点项目(CQcstc2013jjB40008)

详细信息

作者简介:
胡进(1980—),男,湖北襄阳人, 讲师,博士(E-mail: victorjhu@gmail.com);宋乾坤(1963—),男,教授,博士(通讯作者. E-mail:qiankunsong@163.com).

中图分类号: O175.13
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- 文章访问数: 1651
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出版历程
- 收稿日期: 2013-05-07
- 修回日期: 2013-05-09
- 刊出日期: 2013-07-15

Global Uniform Asymptotic Stability of Memristor-Based Recurrent Neural Networks With Time Delays

Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, P.R.China

摘要

摘要: 忆阻是近年来新发现的一类非线性电子元件．与通常的电阻不同，忆阻的阻值会随着通过的电流量的大小和方向不同而改变．这个特性使得忆阻具有了记忆的功能，在很多方面有着广泛的应用．该文给出了简化的忆阻的数学模型，基于该模型构造了时滞神经网络，利用微分包含理论、Lyapunov方法和同胚映射原理研究了其全局渐近稳定性问题，确保模型平衡点存在性、唯一性和一致全局渐近稳定性的充分条件被获得．最后提供的具有仿真的例子验证了获得的理论结果．
- 无腹筋钢筋混凝土梁 /
- 剪切强度 /
- 极限平衡法 /
- 尺寸效应 /
- 临界剪压区高度 /
- 应力分布
Abstract: Memristor is a newly prototyped nonlinear circuit device. Its value is not unique and changes according to the value of the magnitude and polarity of the voltage applied to it. Due to this feature, the memristor has the function of memory and broad potential applications of memristors have been reported in various fields. A simplified mathematical model was proposed to characterize the pinched hysteresis feature of the memristor and a memristor-based recurrent neural network model was given. With the theory of differential inclusion, Lyapunov approach and homeomorphism theory, the existence and uniqueness of the equilibrium point of the model were obtained, and the global uniform asymptotic stability of memristor-based recurrent neural networks was also obtained. Finally, the simulation result shows the efficiency of the theorem.
- memristor /
- recurrent neural network /
- global uniform asymptotic stability /

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参考文献(24)

[1]	Strukov D B, Snider G S, Stewart D R, Williams R S. The missing memristor found[J].Nature,2008, 453(7191): 80-83.
[2]	Chua L O. Memristor the missing circuit element[J].IEEE Transactions on Circuit Theory,1971, 18(5): 507-519.
[3]	Pershin Y V, Ventra M D. Spin memristive systems: spin memory effects in semiconductor spintronics[J].Physical Review B,2008, 78(11): 1-4.
[4]	Yang J J, Pickett M D, Li X, Ohlberg D A A, Stewart D R, Williams R S.Memristive switching mechanism for metal/oxide/metal nanodevices[J].Nature Nanotechnology,2008, 3(7): 429-433.
[5]	Wang X, Chen Y, Xi H, Li H, Dimitrov D. Spintronic memristor through-spin-torqueinduced magnetization motion[J].IEEE Electron Device Letters,2009, 30(3): 294-297.
[6]	Xia Y, Wang J. Global asymptotic and exponential stability of a dynamic-neural system with asymmetric connection weights[J].IEEE Transactions on Automatic Control,2001, 46(4): 635-638.
[7]	Hu S, Wang J. Global asymptotic stability and global exponential stability of continuous-time recurrent neural networks[J].IEEE Transactions on Automatic Control,2002, 46(5):802-807.
[8]	Cao J, Wang J. Global asymptotic stability of a general class of recurrent neural network with time-varing delays[J].IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2003, 50(1): 34-44.
[9]	Zhang J. Globally exponential stability of neural networks with variable delays[J].IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2003, 50(2): 288-291.
[10]	Zeng Z, Wang J, Liao X. Global exponential stability of a general class of recurrent neural networks with timevarying delays[J].IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003, 50(10): 1353-1358.
[11]	Cao J, Wang J. Global asymptotic and robust stability of recurrent neural networks with time delays[J].IEEE Transactions on Circuits and Systems I: Regular Papers,2005, 52(2): 417-426.
[12]	Liao X, Wang J, Zeng Z. Global asymptotic stability and global exponential stability of delayed cellular neural networks[J].IEEE Transactions on Circuits and Systems II: Express Briefs,2005, 52(7): 168-173.
[13]	Zeng Z, Wang J, Liao X. Global asymptotic stability and global exponential stability of neural networks with unbounded time-varying delays[J].IEEE Transactions on Circuits and Systems II: Express Briefs,2005, 52(3): 403-409.
[14]	Cao J, Yuan K, Li H. Global asymptotical stability of recurrent neural-networks with multiple discrete delays and distributed delays[J].IEEE Transactions on Neural Networks,2006, 17(6): 1646-1651.
[15]	Zeng Z, Wang J. Improved conditions for global exponential stability of recurrent neural networks with timevarying delays[J].IEEE Transactions on Neural Networks,2006, 17(3): 623-635.
[16]	Chen W, Zheng W. Global asymptotic stability of a class of neural networks with distributed delays[J].IEEE Transactions on Circuits and Systems I: Regular Papers,2006, 53(3): 244-252.
[17]	Yu W, Cao J, Wang J. An LMI approach to delayed global asymptotic stability of the Cohen-Grossberg neural networks via nonsmooth analysis[J]. Neural Networks,2007, 20(7): 810-818.
[18]	Chen W, Zheng W. On global asymptotic stability of Cohen-Grossberg neural networks with variable delays[J].IEEE Transactions on Circuits and Systems I: Regular Papers,2008, 55(10): 3145-3159.
[19]	Shen Y, Wang J. An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays[J].IEEE Transactions on Neural Networks,2008, 19(3): 528-531.
[20]	Filippov A F.Differential Equations With Discontinuous Right-Hand-Sides [M]. Dordrecht: Kluwer, 1988.
[21]	Paden B E, Sastry S S. A calculus for computing Filippov’s differential inclusions with applications to the variable structure control of robot manipulators[J].IEEE Transactions on Circuits and Systems,1987, 34(1): 73-82.
[22]	Bacciotti A, Rosier L.Liapunov Functions and Stability in Control Theory [M]. 2nd ed. Communications and Control Engineering. Vol 14. London: Springer, 2005.
[23]	Forti M, Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems[J].IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications,1995, 42(7): 354-366.
[24]	Berman A, Plemmons R J.Nonnegative Matrices in the Mathematical Sciences [M].New York: Academic Press, 1979.

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基于忆阻的时滞神经网络的全局稳定性

doi: 10.3879/j.issn.1000-0887.2013.07.007

作者简介:
胡进(1980—),男,湖北襄阳人, 讲师,博士(E-mail: victorjhu@gmail.com);宋乾坤(1963—),男,教授,博士(通讯作者. E-mail:qiankunsong@163.com).

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Global Uniform Asymptotic Stability of Memristor-Based Recurrent Neural Networks With Time Delays

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基于忆阻的时滞神经网络的全局稳定性

doi: 10.3879/j.issn.1000-0887.2013.07.007

作者简介: 胡进(1980—),男,湖北襄阳人, 讲师,博士(E-mail: victorjhu@gmail.com);宋乾坤(1963—),男,教授,博士(通讯作者. E-mail:qiankunsong@163.com).

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出版历程

Global Uniform Asymptotic Stability of Memristor-Based Recurrent Neural Networks With Time Delays

计量

出版历程

目录

作者简介:
胡进(1980—),男,湖北襄阳人, 讲师,博士(E-mail: victorjhu@gmail.com);宋乾坤(1963—),男,教授,博士(通讯作者. E-mail:qiankunsong@163.com).