Global Exponential Stability of Modified RTD-based Two-Neuron Networks with Discrete Time Delays

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姓名

陳宣伃(Hsuan-Yu Chen) 查詢紙本館藏

畢業系所

數學系

論文名稱

(Global Exponential Stability of Modified RTD-based Two-Neuron Networks with Discrete Time Delays)

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摘要(中)

論文摘要
這篇論文主要研究離散時間遲滯的修正型RTD 雙神經元網路之全局指數穩定。在加入三種不同邊界條件後得到三組修正型RTD 雙神經元細胞網路( DCNNs )的微分方程；每一組微分方程都包含了兩個相似的細胞，每個細胞都有非線性瞬時的自身回饋，並藉由Lipshitz非線性性質與其他細胞互相連結，但卻有不同的離散時間遲滯。每組微分方程都包含外界的輸入，在自身回饋及細胞間連結長度加入適當條件後，建造適當的Lyapunov functionals ，可以驗證出其唯一平衡點具有全局指數穩定的特性；若是給定週期之外界輸入，則可驗證出每
組微分方程的週期解也具有全局指數穩定的特性。最後我們也搭配一些數值結果來驗證理論分析。

摘要(英)

Abstract
In this thesis, we study the global exponential stability of the modi¯ed RTD-based two-neuron networks with discrete time delays. After imposing the periodic, Dirichlet or Neumann boundary conditions, the resulting systems consist of two identical neurons, each possessing nonlinear instantaneous self-feedback
and connected to the other neuron via a Lipschitz nonlinearity but with di®erent
discrete time delays. For each two-neuron system with constant external inputs, under appropriate conditions on the self-feedback and connection strengths, we prove the unique equilibrium is globally exponentially stable by constructing a
suitable Lyapunov functional. On the other hand, for such two-neuron systems with periodic external inputs, combining the techniques of Lyapunov functional with the contraction mapping theorem, we propose some su±cient conditions
for establishing the existence, uniqueness and global exponential stability of the periodic solutions. Numerical results are also provided to demonstrate the theoretical analyses.

關鍵字(中)

關鍵字(英)

★ equilibrium
★ periodic solution
★ global exponential stability
★ Lyapunov functional
★ discrete time delay
★ contraction mapping theorem
★ cellular neural network

論文目次

Contents
² Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 1
² Periodic boundary condition . . . . . .. . . . . . . . . . . . . 3
² Dirichlet boundary condition . . . . . . . . . . . . . . . . . 13
² Neumann boundary condition . . . . .. . . . . . . . . . . . . . 17
² Concluding remarks . . . . . . . . .. . . . . . . . . . . . . . 22
² References . . . . . . . . . . . . . . . . . . . . . . . . . . 23

參考文獻

References
[1] J. Cao and Q. Li, On the exponential stability and periodic solutions of
delayed cellular neural networks, J. Math. Anal. Appl., 252 (2000), pp.50-64.
[2] J. Cao and D. Zhou, Stability analysis of delayed cellular neural networks
Neural networks, 11 (1998), pp. 1601-1605.
[3] L. O. Chua, CNN: A Paradigm for Complexity, World Scienti¯c Series on
Nonlinear Science, Series A, Vol. 31, World Scienti¯c, Singapore, 1998.
[4] L. O. Chua and L. Yang, Cellular neural networks: Theory, IEEE Trans.
Circuits Syst., 35 (1988), pp. 1257-1272.
[5] L. O. Chua and L. Yang, Cellular neural networks: Applications, IEEE
Trans. Circuits Syst., 35 (1988), pp.1273-1290.
[6] P. van den Driessche, J. Wu, and X. Zou, Stabilization role of inhibitory
self-connections in a delayed neural network, Physica D, 150 (2001), pp.
84-90.
[7] P. van den Driessche and X. Zou, Global attractivity in delayed Hop¯eld
neural network models, SIAM J. Appl. Math., 58 (1998), pp. 1878-1890.
[8] K. Gopalsamy and X.-Z. He, Stability in asymmetric Hop¯eld nets with
transmission delays, Physcia D, 76 (1994), pp. 344-358.
[9] K. Gopalsamy and I. Leung, Delay induced periodicity in a neural netlet
of excitation and inhibition, Physcia D, 89 (1996), pp. 395-426.
[10] C.-H. Hsu and S.-S. Lin, Existence and multiplicity of traveling waves in a lattice dynamical system, J. Di®. Eqns., 164 (2000), pp. 431-450.
[11] C.-H. Hsu, S.-S. Lin and W. Shen, Traveling waves in cellular neural net-
works, Internat. J. Bifur. and Chaos, 9 (1999), pp. 1307-1319.
[12] C.-H. Hsu and S.-Y. Yang, On camel-like traveling wave solutions in cellular neural networks, J. Di®. Eqns., 196 (2004), pp. 481-514.
[13] C.-H. Hsu and S.-Y. Yang, Wave propagation in RTD-based cellular neural
networks, J. Di®. Eqns., 204 (2004), pp. 339-379.
[14] C.-H. Hsu and S.-Y. Yang, Structure of a class of traveling waves in delayed cellular neural networks, DCDS, Series A, 13 (2005), pp. 339-359.
[15] C.-H. Hsu and S.-Y. Yang, Existence of monotonic traveling waves in mod-
i¯ed RTD-based cellular neural networks, to appear in DCDS, Expanded
Volume.
[16] C.-H. Hsu, S.-Y. Yang, T.-H. Yang, and T.-S. Yang, On periodic solutions
of a two-neuron network system with sigmoidal activation functions, to
appear in Internat. J. Bifur. and Chaos.
[17] M. Itoh, P. Julian, and L. O. Chua, RTD-based cellular neural networks
with multiple steady states, Internat. J. Bifur. and Chaos, 11 (2001), pp.
2913-2959.
[18] J. Juang and S.-S. Lin, Cellular neural networks: mosaic pattern and spa-
tial chaos, SIAM J. Appl. Math., 60 (2000), pp. 891-915.
[19] P. Weng and J. Wu, Deformation of traveling waves in delayed cellular
neural networks, Internat. J. Bifur. and Chaos, 13 (2003), pp. 797-813.

指導教授

楊肅煜(Suh-Yuh Yang)

審核日期

2005-7-13

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