
Previous Article
Long time dynamics near the symmetry breaking bifurcation for nonlinear Schrödinger/GrossPitaevskii equations
 DCDS Home
 This Issue

Next Article
Global existence for high dimensional quasilinear wave equations exterior to starshaped obstacles
Stable and unstable periodic orbits in complex networks of spiking neurons with delays
1.  Center for Brain Science, Faculty of Arts and Sciences, Harvard University, Cambridge, MA, United States 
2.  Network Dynamics Group, Max Planck Institute for Dynamics & SelfOrganization (MPIDS), Göttingen, Bernstein Center for Computational Neuroscience (BCCN) Göttingen, Department of Physics, Georg August University, Göttingen, Germany 
[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 
[2] 
Karim El Laithy, Martin Bogdan. Synaptic energy drives the information processing mechanisms in spiking neural networks. Mathematical Biosciences & Engineering, 2014, 11 (2) : 233256. doi: 10.3934/mbe.2014.11.233 
[3] 
Pierre Guiraud, Etienne Tanré. Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size. Discrete & Continuous Dynamical Systems  B, 2019, 24 (9) : 51835201. doi: 10.3934/dcdsb.2019056 
[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 
[5] 
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 
[6] 
Tingting Su, Xinsong Yang. Finitetime synchronization of competitive neural networks with mixed delays. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 36553667. doi: 10.3934/dcdsb.2016115 
[7] 
Benedetta Lisena. Average criteria for periodic neural networks with delay. Discrete & Continuous Dynamical Systems  B, 2014, 19 (3) : 761773. doi: 10.3934/dcdsb.2014.19.761 
[8] 
Ricai Luo, Honglei Xu, WuSheng Wang, Jie Sun, Wei Xu. A weak condition for global stability of delayed neural networks. Journal of Industrial & Management Optimization, 2016, 12 (2) : 505514. doi: 10.3934/jimo.2016.12.505 
[9] 
LeongKwan Li, Sally Shao, K. F. Cedric Yiu. Nonlinear dynamical system modeling via recurrent neural networks and a weighted state space search algorithm. Journal of Industrial & Management Optimization, 2011, 7 (2) : 385400. doi: 10.3934/jimo.2011.7.385 
[10] 
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 
[11] 
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 
[12] 
Ying Sue Huang. Resynchronization of delayed neural networks. Discrete & Continuous Dynamical Systems  A, 2001, 7 (2) : 397401. doi: 10.3934/dcds.2001.7.397 
[13] 
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 
[14] 
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 
[15] 
Yong Zhao, Qishao Lu. Periodic oscillations in a class of fuzzy neural networks under impulsive control. Conference Publications, 2011, 2011 (Special) : 14571466. doi: 10.3934/proc.2011.2011.1457 
[16] 
Sylvia Novo, Rafael Obaya, Ana M. Sanz. Exponential stability in nonautonomous delayed equations with applications to neural networks. Discrete & Continuous Dynamical Systems  A, 2007, 18 (2&3) : 517536. doi: 10.3934/dcds.2007.18.517 
[17] 
Ruoxia Li, Huaiqin Wu, Xiaowei Zhang, Rong Yao. Adaptive projective synchronization of memristive neural networks with timevarying delays and stochastic perturbation. Mathematical Control & Related Fields, 2015, 5 (4) : 827844. doi: 10.3934/mcrf.2015.5.827 
[18] 
Benoît Perthame, Delphine Salort. On a voltageconductance kinetic system for integrate & fire neural networks. Kinetic & Related Models, 2013, 6 (4) : 841864. doi: 10.3934/krm.2013.6.841 
[19] 
JinLiang Wang, ZhiChun Yang, Tingwen Huang, Mingqing Xiao. Local and global exponential synchronization of complex delayed dynamical networks with general topology. Discrete & Continuous Dynamical Systems  B, 2011, 16 (1) : 393408. doi: 10.3934/dcdsb.2011.16.393 
[20] 
Tatyana S. Turova. Structural phase transitions in neural networks. Mathematical Biosciences & Engineering, 2014, 11 (1) : 139148. doi: 10.3934/mbe.2014.11.139 
2018 Impact Factor: 1.143
Tools
Metrics
Other articles
by authors
[Back to Top]