Global Exponential Periodicity of Discrete-Time Complex-Valued Neural Networks With Time-Delays
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摘要: 复值神经网络是神经网络的一个分支,也是最近几年快速发展的一个领域,在图像处理、模式识别、联想记忆等方面有广泛的应用.目前,对于复值神经网络动力学方面的研究主要集中在稳定性上,对于离散时间型复值神经网络周期性的研究还几乎没有.首先将连续时间型复值神经网络模型离散化得到离散时间型复值神经网络模型,然后利用M矩阵理论、不等式技巧和Lyapunov方法,获得了全局指数周期性的一个充分条件,最后给出的具有仿真的数值例子验证了获得结果的有效性.Abstract: Since the last decade, complex-valued neural networks have been rapidly developed and applied in various research areas, but few research has been done on the periodicity on discrete-time complex-valued neural networks.The periodicity of discrete-time complex-valued neural networks with time-delays was investigated.With the discretization technique, the discrete-time analogue of the continuous-time system with periodic input was formulated, and a sufficient condition for checking the global exponential periodicity of the considered neural networks was obtained. Numeric simulation verifieds validity of the analysis.
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[1] Cao J. Periodic oscillation and exponential stability of delayed CNNs[J]. Phyics Letter A,2000,270(3/4): 157-163. [2] Cao J, Wang J. Global exponential stability and periodicity of recurrent-neural networks with time delays[J]. IEEE Transactions on Circuits and SystemsI: Regular Papers,2005,52(5): 920-931. [3] Chen B, Wang J. Global exponential periodicity of a class of recurrent-neural networks with oscillating parameters and timevarying delays[J]. IEEE Transactions on Neural Networks,2005,16(6): 1440-1448. [4] Chen T. Global exponential stability of delayed Hopfield neural networks[J]. Neural Networks,2001,14(8): 977-980. [5] Ji Y. Global attractivity of almost periodic sequence solutions of delayed discretetime neural networks[J]. Arabian Journal for Science and Engineering,2011,36(7): 1447-1459. [6] Li C, Liao X, Yu J. Complex valued recurrent neural network with IIR neural model: training and applications[J]. Circuits Systems Signal Processing,2002,21(5): 461-471. [7] Liao X, Wang L, Yu P. Stability of Dynamical Systems [M]. Vol 5. Monograph Series on Nonlinear Science and Complexity.Amsterdam, The Netherlands: Elsevier, 2007. [8] Mohamad S, Gopalsamy K. Dynamics of a class of discrete-time neural-networks and their continuous-time counterparts[J]. Mathematics and Computers in Simulation,2000,53(1/2): 1-39. [9] Sun C, Feng C B. Exponential periodicity of continuous-time and discrete-time neural networks with delays[J]. Neural Processing Letters,2004,19(2): 131-146. [10] Bohner M, Rao V S H, Sanyal S. Global stability of complex-valued-neural networks on time scales[J]. Differential Equations and Dynamical Systems,2011,19(1/2): 3-11. [11] Hirose A. Complex-Valued Neural Networks: Theories and Applications [M].Singapore: World Scientific, 2003. [12] Hirose A. Complex-Valued Neural Networks [M]. Heidelberg, German: Springer, 2006. [13] Hu J, Wang J. Global stability of complex-valued recurrent neural-networks with time-delays[J]. IEEE Transcations on Neural Networks and Learning Systems,2012,23(6): 853-865. [14] Jankowski S, Lozowski A, Zurada J. Complex-valued multistate neural-associative memory[J]. IEEE Transactions on Neural Networks,1996,7(6): 1491-1496. [15] Lee D L. Improving the capacity of complex-valued neural networks with a modified gradient descent learning rule[J]. IEEE Transactions on Neural Networks,2001,12(2): 439-443. [16] Lee D L. Relaxation of the stability condition of the complex-valued neural networks[J]. IEEE Transactions on Neural Networks,2001,12(5): 1260-1262. [17] Rudin R. Real and Complex Analysis [M]. New York: McGrawHill, 1987. [18] DUAN Cheng-jun, SONG Qian-kun. Boundedness and stability for discrete-time delayed neural network with complex-valued linear threshold neurons[J]. Discrete Dynamics in Nature and Society,2010,2010: 1-19. [19] Kobayashi M. Exceptional reducibility of complex-valued neural networks[J]. IEEE Transactions on Neural Networks,2010,21(7): 1060-1072. [20] Berman A, Plemmons R J. Nonnegative Matrices in the Mathematical Sciences [M]. New York: Academic Press, 1979.
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