Stability Analysis of Delayed Cellular Neural Networks With and Without Noise Perturbation
-
摘要: 分析了一类时滞细胞神经网络(DCNN)系统在无噪声和有噪声干扰情况下的稳定性.首先针对确定性系统给出了一种简单且容易验证的全局指数稳定性条件,然后讨论了噪声干扰下系统的稳定性.当DCNN被外部噪声扰动时,系统是全局稳定的.重要的是,当系统被内在噪声扰动时,只要噪声总强度控制在一定范围内,系统是全局指数稳定的.鉴于随机共振现象在越来越多的非线性生物系统中被发现,这种稳定性具有重要意义.Abstract: The stability of a class of delayed cellular neural networks (DCNN) either without or with noise perturbation are studied. After presenting a simple and easily checkable condition for global exponential stability of the deterministic system, the situations with noise perturbation were further investigated. When the DCNN is perturbed with an external noise, the system is globally stable. The important fact is that, when the system is perturbed with an internal noise, it's globally exponentially stable if only the total strength of the noise is within a certain bound. This fact is significant as stochastic resonance phenomena have been found exist in many nonlinear systems.
-
[1] Chua L O,Yang L.Cellular neural networks: theory[J].IEEE Trans Circuits and Systems,1988,35(10):1257-1272. doi: 10.1109/31.7600 [2] Chua L O,Yang Y.Cellular neural networks:applications[J].IEEE Trans Circuits and Systems,1988,35(10):1273-1290. doi: 10.1109/31.7601 [3] Roska T,Chua L O.Cellular neural networks with nonlinear and delay-type template elements and nonuniform grids[J].International Journal of Circuit Theory and Applications,1992,20(5):469-481. doi: 10.1002/cta.4490200504 [4] Roska T,Wu C W,Balsi M,et al.Stability and dynamics of delay-type general and cellular neural networks[J].IEEE Transactions on Circuits and Systems—Ⅰ: Fundamental Theory and Applications,1992,39(6):487-490. doi: 10.1109/81.153647 [5] Cilli P P,Gilli M.On stability of cellular neural networks with delay [J].IEEE Transactions on Circuits and Systems—Ⅰ: Fundamental Theory and Applications,1993,40(3):157-165. doi: 10.1109/81.222796 [6] Gilli M.Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions[J].IEEE Transactions on Circuits and Systems—Ⅰ: Fundamental Theory and Applications,1994,41(8):518-528. doi: 10.1109/81.311541 [7] Lu H,He Y,He Z.A chaos-generator: analyses of complex dynamics of a cell equation in delayed cellular neural networks[J].IEEE Transactions on Circuits and Systems—Ⅰ:Fundamental Theory and Applications,1998,45(2):178-181. doi: 10.1109/81.661687 [8] Zhou D,Cao J.Globally exponential stability conditions for cellular neural networks with time-varying delay[J].Applied Mathematics and Computation,2002,131(2/3):487-496. doi: 10.1016/S0096-3003(01)00162-X [9] Cao J.Global stability analysis in delayed cellular neural networks[J].Phys Rev E,1999,59(5):5940-5944. doi: 10.1103/PhysRevE.59.5940 [10] Cao J.A set of stability criteria for delayed cellular neural networks[J].IEEE Transactions on Circuits and Systems—Ⅰ: Fundamental Theory and Applications,2001,48(4):494-498. doi: 10.1109/81.917987 [11] Zhang Y,Pheng A H,Kwong S L.Convergence analysis of cellular neural networks with unbounded delay[J].IEEE Transactions on Circuits and Systems—Ⅰ: Fundamental Theory and Applications,2001,48(6):680-687. doi: 10.1109/81.928151 [12] Zhang Y,Heng P A,Vadakkepat P.Absolute periodicity and absolute stability of neural networks with delays[J].IEEE Transactions on Circuits and Systems—Ⅰ:Fundamental Theory and Applications,2002,49(2):256-261. doi: 10.1109/81.983875 [13] Dunkel J,Hilbert S,Schimansky-Geier L,et al.Stochastic resonance in biological nonlinear evolution models[J].Phys Rev E,2004,69(5):056118,13. doi: 10.1103/PhysRevE.69.056118 [14] Machura L,Kostur M,Talkner P,et al.Brownian motors: current fluctuations and rectification efficiency[J].Phys Rev E,2004,70(6):061105,8. doi: 10.1103/PhysRevE.70.061105 [15] Reimann P.Brownian motors:noisy transport far from equilibrum[J].Physics Reports,2002,361(2/4):257-265.
点击查看大图
计量
- 文章访问数: 2472
- HTML全文浏览量: 90
- PDF下载量: 731
- 被引次数: 0