
Previous Article
Multiobjective aggregate production planning decisions using twophase fuzzy goal programming method
 JIMO Home
 This Issue

Next Article
An integrated approach for the operations of distribution and lateral transshipment for seasonal products  A case study in household product industry
Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm
1.  Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China 
2.  Department of Mathematics, Cleveland State University, Cleveland, OH 44115, United States 
References:
[1] 
A. F. Atiya and A. G. Parlos, New results on recurrent network training: Unifying the algorithms and accelerating convergence,, IEEE Transcations on Neural Networks, 11 (2000), 697. doi: 10.1109/72.846741. Google Scholar 
[2] 
Y. Fang and T. W. S. Chow, Nonlinear dynamical systems control using a new RNN temporal learning strategy,, IEEE Trans on Circuit and Systems, 52 (2005), 719. Google Scholar 
[3] 
R. A. Conn, K. Scheinberg and N. L. Vicente, "Introduction to Derivativefree Optimization,", SIAM, (2009). doi: 10.1137/1.9780898718768. Google Scholar 
[4] 
J. F. G. Freitas, M. Niranjan, A. H. Gee and A. Doucet, Sequential Monte Carlo methods to train neural network models,, Neural Computation, 12 (2000), 955. doi: 10.1162/089976600300015664. Google Scholar 
[5] 
L. K. Li, Learning sunspot series dynamics by recurrent neural networks,, in, (2003), 107. doi: 10.1142/9789812704955_0009. Google Scholar 
[6] 
L. K. Li, W. K. Pang, W. T. Yu and M. D. Trout, Forecasting shortterm exchange Rates: a recurrent neural network approach,, in, (2004), 195. doi: 10.4018/9781591401766.ch010. Google Scholar 
[7] 
L. K. Li and S. Shao, Dynamic properties of recurrent neural networks and its approximations,, International Journal of Pure and Applied Mathematics, 39 (2007), 545. Google Scholar 
[8] 
L. K. Li and S. Shao, A neural network approach for global optimization with applications,, Neural Network World, 18 (2008), 365. Google Scholar 
[9] 
L. K. Li, S. Shao and T. Zheleva, A state space search algorithm and its application to learn the shortterm foreign exchange rates,, Applied Mathematical Sciences, 2 (2008), 1705. Google Scholar 
[10] 
X. D. Li, J. K. L. Ho and T. W. S. Chow, Approximation of dynamical timevariant systems by continuoustime recurrent neural networks,, IEEE Trans on Circuit and Systems, 52 (2005), 656. Google Scholar 
[11] 
X. B. Liang and J. Wang, A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints,, IEEE Transactions on Neural Networks, 11 (2000), 1251. doi: 10.1109/72.883412. Google Scholar 
[12] 
Z. Liu and I. Elhanany, A Fast and Scalable Recurrent Neural Network Based on Stochastic Meta Descent,, IEEE Transactions on Neural Networks, 19 (2008), 1652. doi: 10.1109/TNN.2008.2000838. Google Scholar 
[13] 
S. Wang, Q. Shao and X. Zhou, Knotoptimizing spline networks (KOSNETS) for nonparametric regression,, Journal of Industrial and Management Optimization, 4 (2008). Google Scholar 
[14] 
X. Wang and E. K. Blum, Discretetime versus continuoustime models of neural networks,, Journal of Computer and System Sciences, 45 (1992), 1. doi: 10.1016/00220000(92)90038K. Google Scholar 
[15] 
R. J. Williams and D. Zipser, A learning algorithm for continually running fully recurrent neural networks,, Neural Computation, 1 (1989), 270. doi: 10.1162/neco.1989.1.2.270. Google Scholar 
[16] 
L. Xu and W. Liu, A new recurrent neural network adaptive approach for hostgate way rate control protocol within intranets using ATM ABR service,, Journal of Industrial and Management Optimization, 1 (2005), 389. Google Scholar 
[17] 
J. Yao and C. L. Tan, A case study on using neural networks to perform technical forecasting of forex,, Neural Computation, 34 (2000), 79. Google Scholar 
[18] 
K. F. C. Yiu, S. Wang, K. L. Teo and A. H. Tsoi, Nonlinear system modeling via knotoptimizing Bspline networks,, IEEE Transactions on Neural Networks, 12 (2001), 1013. doi: 10.1109/72.950131. Google Scholar 
[19] 
K. F. C. Yiu, Y. Liu and K. L. Teo, A hybrid descent method for global optimization,, Journal of Global Optimization, 28 (2004), 229. doi: 10.1023/B:JOGO.0000015313.93974.b0. Google Scholar 
show all references
References:
[1] 
A. F. Atiya and A. G. Parlos, New results on recurrent network training: Unifying the algorithms and accelerating convergence,, IEEE Transcations on Neural Networks, 11 (2000), 697. doi: 10.1109/72.846741. Google Scholar 
[2] 
Y. Fang and T. W. S. Chow, Nonlinear dynamical systems control using a new RNN temporal learning strategy,, IEEE Trans on Circuit and Systems, 52 (2005), 719. Google Scholar 
[3] 
R. A. Conn, K. Scheinberg and N. L. Vicente, "Introduction to Derivativefree Optimization,", SIAM, (2009). doi: 10.1137/1.9780898718768. Google Scholar 
[4] 
J. F. G. Freitas, M. Niranjan, A. H. Gee and A. Doucet, Sequential Monte Carlo methods to train neural network models,, Neural Computation, 12 (2000), 955. doi: 10.1162/089976600300015664. Google Scholar 
[5] 
L. K. Li, Learning sunspot series dynamics by recurrent neural networks,, in, (2003), 107. doi: 10.1142/9789812704955_0009. Google Scholar 
[6] 
L. K. Li, W. K. Pang, W. T. Yu and M. D. Trout, Forecasting shortterm exchange Rates: a recurrent neural network approach,, in, (2004), 195. doi: 10.4018/9781591401766.ch010. Google Scholar 
[7] 
L. K. Li and S. Shao, Dynamic properties of recurrent neural networks and its approximations,, International Journal of Pure and Applied Mathematics, 39 (2007), 545. Google Scholar 
[8] 
L. K. Li and S. Shao, A neural network approach for global optimization with applications,, Neural Network World, 18 (2008), 365. Google Scholar 
[9] 
L. K. Li, S. Shao and T. Zheleva, A state space search algorithm and its application to learn the shortterm foreign exchange rates,, Applied Mathematical Sciences, 2 (2008), 1705. Google Scholar 
[10] 
X. D. Li, J. K. L. Ho and T. W. S. Chow, Approximation of dynamical timevariant systems by continuoustime recurrent neural networks,, IEEE Trans on Circuit and Systems, 52 (2005), 656. Google Scholar 
[11] 
X. B. Liang and J. Wang, A recurrent neural network for nonlinear optimization with a continuously differentiable objective function and bound constraints,, IEEE Transactions on Neural Networks, 11 (2000), 1251. doi: 10.1109/72.883412. Google Scholar 
[12] 
Z. Liu and I. Elhanany, A Fast and Scalable Recurrent Neural Network Based on Stochastic Meta Descent,, IEEE Transactions on Neural Networks, 19 (2008), 1652. doi: 10.1109/TNN.2008.2000838. Google Scholar 
[13] 
S. Wang, Q. Shao and X. Zhou, Knotoptimizing spline networks (KOSNETS) for nonparametric regression,, Journal of Industrial and Management Optimization, 4 (2008). Google Scholar 
[14] 
X. Wang and E. K. Blum, Discretetime versus continuoustime models of neural networks,, Journal of Computer and System Sciences, 45 (1992), 1. doi: 10.1016/00220000(92)90038K. Google Scholar 
[15] 
R. J. Williams and D. Zipser, A learning algorithm for continually running fully recurrent neural networks,, Neural Computation, 1 (1989), 270. doi: 10.1162/neco.1989.1.2.270. Google Scholar 
[16] 
L. Xu and W. Liu, A new recurrent neural network adaptive approach for hostgate way rate control protocol within intranets using ATM ABR service,, Journal of Industrial and Management Optimization, 1 (2005), 389. Google Scholar 
[17] 
J. Yao and C. L. Tan, A case study on using neural networks to perform technical forecasting of forex,, Neural Computation, 34 (2000), 79. Google Scholar 
[18] 
K. F. C. Yiu, S. Wang, K. L. Teo and A. H. Tsoi, Nonlinear system modeling via knotoptimizing Bspline networks,, IEEE Transactions on Neural Networks, 12 (2001), 1013. doi: 10.1109/72.950131. Google Scholar 
[19] 
K. F. C. Yiu, Y. Liu and K. L. Teo, A hybrid descent method for global optimization,, Journal of Global Optimization, 28 (2004), 229. doi: 10.1023/B:JOGO.0000015313.93974.b0. Google Scholar 
[1] 
LeongKwan Li, Sally Shao. Convergence analysis of the weighted state space search algorithm for recurrent neural networks. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 193207. doi: 10.3934/naco.2014.4.193 
[2] 
K. L. Mak, J. G. Peng, Z. B. Xu, K. F. C. Yiu. A novel neural network for associative memory via dynamical systems. Discrete & Continuous Dynamical Systems  B, 2006, 6 (3) : 573590. doi: 10.3934/dcdsb.2006.6.573 
[3] 
Lixin Xu, Wanquan Liu. A new recurrent neural network adaptive approach for hostgate way rate control protocol within intranets using ATM ABR service. Journal of Industrial & Management Optimization, 2005, 1 (3) : 389404. doi: 10.3934/jimo.2005.1.389 
[4] 
Sanjay K. Mazumdar, ChengChew Lim. A neural network based antiskid brake system. Discrete & Continuous Dynamical Systems  A, 1999, 5 (2) : 321338. doi: 10.3934/dcds.1999.5.321 
[5] 
Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure & Applied Analysis, 2009, 8 (2) : 655671. doi: 10.3934/cpaa.2009.8.655 
[6] 
Vena Pearl Bongolanwalsh, David Cheban, Jinqiao Duan. Recurrent motions in the nonautonomous NavierStokes system. Discrete & Continuous Dynamical Systems  B, 2003, 3 (2) : 255262. doi: 10.3934/dcdsb.2003.3.255 
[7] 
Ying Sue Huang, Chai Wah Wu. Stability of cellular neural network with small delays. Conference Publications, 2005, 2005 (Special) : 420426. doi: 10.3934/proc.2005.2005.420 
[8] 
King Hann Lim, Hong Hui Tan, Hendra G. Harno. Approximate greatest descent in neural network optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 327336. doi: 10.3934/naco.2018021 
[9] 
ShyanShiou Chen, ChihWen Shih. Asymptotic behaviors in a transiently chaotic neural network. Discrete & Continuous Dynamical Systems  A, 2004, 10 (3) : 805826. doi: 10.3934/dcds.2004.10.805 
[10] 
Ndolane Sene. Fractional input stability and its application to neural network. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 853865. doi: 10.3934/dcdss.2020049 
[11] 
Zhigang Zeng, Tingwen Huang. New passivity analysis of continuoustime recurrent neural networks with multiple discrete delays. Journal of Industrial & Management Optimization, 2011, 7 (2) : 283289. doi: 10.3934/jimo.2011.7.283 
[12] 
Irena Pawłow, Wojciech M. Zajączkowski. Unique solvability of a nonlinear thermoviscoelasticity system in Sobolev space with a mixed norm. Discrete & Continuous Dynamical Systems  S, 2011, 4 (2) : 441466. doi: 10.3934/dcdss.2011.4.441 
[13] 
John R. Tucker. Attractors and kernels: Linking nonlinear PDE semigroups to harmonic analysis statespace decomposition. Conference Publications, 2001, 2001 (Special) : 366370. doi: 10.3934/proc.2001.2001.366 
[14] 
Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367376. doi: 10.3934/proc.2009.2009.367 
[15] 
HuiQiang Ma, NanJing Huang. Neural network smoothing approximation method for stochastic variational inequality problems. Journal of Industrial & Management Optimization, 2015, 11 (2) : 645660. doi: 10.3934/jimo.2015.11.645 
[16] 
Yixin Guo, Aijun Zhang. Existence and nonexistence of traveling pulses in a lateral inhibition neural network. Discrete & Continuous Dynamical Systems  B, 2016, 21 (6) : 17291755. doi: 10.3934/dcdsb.2016020 
[17] 
Jianhong Wu, Ruyuan Zhang. A simple delayed neural network with large capacity for associative memory. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 851863. doi: 10.3934/dcdsb.2004.4.851 
[18] 
Honggang Yu. An efficient face recognition algorithm using the improved convolutional neural network. Discrete & Continuous Dynamical Systems  S, 2019, 12 (4&5) : 901914. doi: 10.3934/dcdss.2019060 
[19] 
Lidong Liu, Fajie Wei, Shenghan Zhou. Major project risk assessment method based on BP neural network. Discrete & Continuous Dynamical Systems  S, 2019, 12 (4&5) : 10531064. doi: 10.3934/dcdss.2019072 
[20] 
Zhuwei Qin, Fuxun Yu, Chenchen Liu, Xiang Chen. How convolutional neural networks see the world  A survey of convolutional neural network visualization methods. Mathematical Foundations of Computing, 2018, 1 (2) : 149180. doi: 10.3934/mfc.2018008 
2018 Impact Factor: 1.025
Tools
Metrics
Other articles
by authors
[Back to Top]