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Asymptotic behaviors in a transiently chaotic neural network
1.  Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan, Taiwan 
[1] 
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 
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Yuantian Xia, Juxiang Zhou, Tianwei Xu, Wei Gao. An improved deep convolutional neural network model with kernel loss function in image classification. Mathematical Foundations of Computing, 2020, 3 (1) : 5164. doi: 10.3934/mfc.2020005 
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Sébastien Guisset. Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and NavierStokes equations. Kinetic & Related Models, 2020, 13 (4) : 739758. doi: 10.3934/krm.2020025 
[4] 
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 
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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 
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Ndolane Sene. Fractional input stability and its application to neural network. Discrete & Continuous Dynamical Systems  S, 2020, 13 (3) : 853865. doi: 10.3934/dcdss.2020049 
[7] 
Wilhelm Schlag. Regularity and convergence rates for the Lyapunov exponents of linear cocycles. Journal of Modern Dynamics, 2013, 7 (4) : 619637. doi: 10.3934/jmd.2013.7.619 
[8] 
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 
[9] 
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 
[10] 
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 
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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 
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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 
[13] 
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 
[14] 
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 
[15] 
Danilo Costarelli, Gianluca Vinti. Asymptotic expansions and Voronovskaja type theorems for the multivariate neural network operators. Mathematical Foundations of Computing, 2020, 3 (1) : 4150. doi: 10.3934/mfc.2020004 
[16] 
Hyeontae Jo, Hwijae Son, Hyung Ju Hwang, Eun Heui Kim. Deep neural network approach to forwardinverse problems. Networks & Heterogeneous Media, 2020, 15 (2) : 247259. doi: 10.3934/nhm.2020011 
[17] 
Hiroaki Uchida, Yuya Oishi, Toshimichi Saito. A simple digital spiking neural network: Synchronization and spiketrain approximation. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 00. doi: 10.3934/dcdss.2020374 
[18] 
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 
[19] 
Regina S. Burachik, C. Yalçın Kaya. An update rule and a convergence result for a penalty function method. Journal of Industrial & Management Optimization, 2007, 3 (2) : 381398. doi: 10.3934/jimo.2007.3.381 
[20] 
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 
2018 Impact Factor: 1.143
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