Global exponential periodicity and stability of discrete-time complex-valued recurrent neural networks with time-delays

Neural Networks - Tập 66 - Trang 119-130 - 2015
Jin Hu1, Jun Wang2
1Department of Mathematics, Chongqing Jiaotong University, Chongqing, China
2Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China

Tài liệu tham khảo

Aizenberg, 2007, Multilayer feedforward neural network based on multi-valued neurons (MLMVN) and a backpropagation learning algorithm, Soft Computing, 11, 169, 10.1007/s00500-006-0075-5 Aizenberg, 2005, A feedforward neural network based on multi-valued neurons, 599 Aizenberg, 2008, Blur identification by multilayer neural network based on multivalued neurons, IEEE Transactions on Neural Networks, 19, 883, 10.1109/TNN.2007.914158 Berman, 1979 Bohner, 2011, Global stability of complex-valued neural networks on time scales, Differential Equations and Dynamical Systems, 19, 3, 10.1007/s12591-010-0076-9 Cao, 2004, Globally exponentially robust stability and periodicity of delayed neural networks, Chaos, Solitons and Fractals, 22, 957, 10.1016/j.chaos.2004.03.019 Cao, 2003, Global asymptotic stability of a general class of recurrent neural network with time-varing delays, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 50, 34, 10.1109/TCSI.2002.807494 Cao, 2005, Global asymptotic and robust stability of recurrent neural networks with time delays, IEEE Transactions on Circuits and Systems. I. Regular Papers, 52, 417, 10.1109/TCSI.2004.841574 Cao, 2005, Global exponential stability and periodicity of recurrent neural networks with time delays, IEEE Transactions on Circuits and Systems. I. Regular Papers, 52, 920, 10.1109/TCSI.2005.846211 Du, 2013, Multistability and multiperiodicity for a general class of delayed Cohen–Grossberg neural networks with discontinuous activation functions, Discrete Dynamics in Nature and Society, 2013, 10.1155/2013/917835 Duan, 2010, Boundedness and stability for discrete-time delayed neural network with complex-valued linear threshold neurons, Discrete Dynamics in Nature and Society, 2010, 1, 10.1155/2010/368379 Goh, 2004, A complex-valued RTRL algorithm for recurrent neural networks, Neural Computation, 16, 2699, 10.1162/0899766042321779 Goh, 2007, An augmented extended Kalman filter algorithm for complex-valued recurrent neural networks, Neural Computation, 19, 1039, 10.1162/neco.2007.19.4.1039 Hirose, 2003, 10.1142/5345 Hirose, 2006 Hirose, 2010, Recent progress in applications of complex-valued neural networks, 42 Hu, 2012, Global stability of complex-valued recurrent neural networks with time-delays, IEEE Transactions on Neural Networks and Learning Systems, 23, 853, 10.1109/TNNLS.2012.2195028 Hu, 2002, Global stability of a class of discrete-time recurrent neural networks, IEEE Transactions on Acoustics, Speech, and Signal Processing Circuits and Systems I: Fundamental Theory and Applications, 48, 1104 Hu, 2006, Global robust stability of a class of discrete-time interval neural networks, IEEE Transactions on Circuits and Systems. I. Regular Papers, 53, 129, 10.1109/TCSI.2005.854288 Huang, 2010, Multistability properties of linear threshold discrete-time recurrent neural networks, International Journal of Information and Systems Sciences, 7, 1 Jankowski, 1996, Complex-valued multistate neural associative memory, IEEE Transactions on Neural Networks, 7, 1491, 10.1109/72.548176 Kobayashi, 2010, Exceptional reducibility of complex-valued neural networks, IEEE Transactions on Neural Networks, 21, 1060, 10.1109/TNN.2010.2048040 Lee, 2001, Improving the capacity of complex-valued neural networks with a modified gradient descent learning rule, IEEE Transactions on Neural Networks, 12, 439, 10.1109/72.914540 Lee, 2001, Relaxation of the stability condition of the complex-valued neural networks, IEEE Transactions on Neural Networks, 12, 1260, 10.1109/72.950156 Lee, 2006, Improvements of complex-valued Hopfield associative memory by using generalized projection rules, IEEE Transactions on Neural Networks, 17, 1341, 10.1109/TNN.2006.878786 Li, 2002, Complex-valued recurrent neural network with IIR neural model: training and applications, Circuits Systems and Signal Processing, 21, 461, 10.1007/s00034-002-0119-8 Liu, X., Fang, K., & Liu, B. (2009). A synthesis method based on stability analysis for complex-valued Hopfield neural network. In Asian control conference (pp. 1245–1250). Mohamad, 2000, Dynamics of a class of discrete-time neural networks and their continuous-time counterparts, Mathematics and Computers in Simulation, 53, 1, 10.1016/S0378-4754(00)00168-3 Mohamad, 2002, Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks, Journal of Computational and Applied Mathematics, 138, 1, 10.1016/S0377-0427(01)00366-1 Nitta, 2003, Solving the XOR problem and the detection of symmetry using a single complex-valued neuron, Neural Networks, 16, 1101, 10.1016/S0893-6080(03)00168-0 Nitta, 2009 Rakkiyappan, 2015, Multiple-stability analysis of complex-valued neural networks with unbounded time-varying delays, Neurocomputing, 149, 594, 10.1016/j.neucom.2014.08.015 Rao, 2008, Global dynamics of a class of complex valued neural networks, International Journal of Neural Systems, 18, 165, 10.1142/S0129065708001476 Stuart, 1996 Sun, 2004, Exponential periodicity of continuous-time and discrete-time neural networks with delays, Neural Processing Letters, 19, 131, 10.1023/B:NEPL.0000023421.60208.30 Wang, 2009, Multistability of neural networks with a class of activation functions, 323 Yan, 2011, Global attractivity of almost periodic sequence solutions of delayed discrete-time neural networks, Arabian Journal for Science and Engineering, 36, 1447, 10.1007/s13369-011-0109-x Zhang, 2009, Activity invariant sets and exponentially stable attractors of linear threshold discrete-time recurrent neural networks, IEEE Transactions on Automatic Control, 54, 1341, 10.1109/TAC.2009.2015552 Zhou, 2009, Discrete-time recurrent neural networks with complex-valued linear threshold neurons, IEEE Transactions on Circuits and Systems II: Express Briefs, 56, 669, 10.1109/TCSII.2009.2025625