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Long time dynamics near the symmetry breaking bifurcation for nonlinear Schrödinger/Gross-Pitaevskii equations
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 & Self-Organization (MPIDS), Göttingen, Bernstein Center for Computational Neuroscience (BCCN) Göttingen, Department of Physics, Georg August University, Göttingen, Germany |
[1] |
Hiroaki Uchida, Yuya Oishi, Toshimichi Saito. A simple digital spiking neural network: Synchronization and spike-train approximation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1479-1494. doi: 10.3934/dcdss.2020374 |
[2] |
Leslaw Skrzypek, Yuncheng You. Feedback synchronization of FHN cellular neural networks. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6047-6056. doi: 10.3934/dcdsb.2021001 |
[3] |
Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Stability of the dynamics of an asymmetric neural network. Communications on Pure and Applied Analysis, 2009, 8 (2) : 655-671. doi: 10.3934/cpaa.2009.8.655 |
[4] |
Karim El Laithy, Martin Bogdan. Synaptic energy drives the information processing mechanisms in spiking neural networks. Mathematical Biosciences & Engineering, 2014, 11 (2) : 233-256. doi: 10.3934/mbe.2014.11.233 |
[5] |
Pierre Guiraud, Etienne Tanré. Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 5183-5201. doi: 10.3934/dcdsb.2019056 |
[6] |
Ndolane Sene. Fractional input stability and its application to neural network. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 853-865. doi: 10.3934/dcdss.2020049 |
[7] |
Ying Sue Huang, Chai Wah Wu. Stability of cellular neural network with small delays. Conference Publications, 2005, 2005 (Special) : 420-426. doi: 10.3934/proc.2005.2005.420 |
[8] |
Tingting Su, Xinsong Yang. Finite-time synchronization of competitive neural networks with mixed delays. Discrete and Continuous Dynamical Systems - B, 2016, 21 (10) : 3655-3667. doi: 10.3934/dcdsb.2016115 |
[9] |
Benedetta Lisena. Average criteria for periodic neural networks with delay. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 761-773. doi: 10.3934/dcdsb.2014.19.761 |
[10] |
Ricai Luo, Honglei Xu, Wu-Sheng Wang, Jie Sun, Wei Xu. A weak condition for global stability of delayed neural networks. Journal of Industrial and Management Optimization, 2016, 12 (2) : 505-514. doi: 10.3934/jimo.2016.12.505 |
[11] |
Leong-Kwan 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 and Management Optimization, 2011, 7 (2) : 385-400. doi: 10.3934/jimo.2011.7.385 |
[12] |
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) : 149-180. doi: 10.3934/mfc.2018008 |
[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 and Continuous Dynamical Systems - B, 2006, 6 (3) : 573-590. doi: 10.3934/dcdsb.2006.6.573 |
[14] |
Ying Sue Huang. Resynchronization of delayed neural networks. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 397-401. doi: 10.3934/dcds.2001.7.397 |
[15] |
Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 |
[16] |
Yong Zhao, Qishao Lu. Periodic oscillations in a class of fuzzy neural networks under impulsive control. Conference Publications, 2011, 2011 (Special) : 1457-1466. doi: 10.3934/proc.2011.2011.1457 |
[17] |
Hotaka Udagawa, Taiji Okano, Toshimichi Saito. Permutation binary neural networks: Analysis of periodic orbits and its applications. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022097 |
[18] |
Ivanka Stamova, Gani Stamov. On the stability of sets for reaction–diffusion Cohen–Grossberg delayed neural networks. Discrete and Continuous Dynamical Systems - S, 2021, 14 (4) : 1429-1446. doi: 10.3934/dcdss.2020370 |
[19] |
Sylvia Novo, Rafael Obaya, Ana M. Sanz. Exponential stability in non-autonomous delayed equations with applications to neural networks. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 517-536. doi: 10.3934/dcds.2007.18.517 |
[20] |
Sanjay K. Mazumdar, Cheng-Chew Lim. A neural network based anti-skid brake system. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 321-338. doi: 10.3934/dcds.1999.5.321 |
2020 Impact Factor: 1.392
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