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Stability, bifurcation analysis in a neural network model with delay and diffusion
1. | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's NL, Canada A1C 5S7, Canada, Canada |
[1] |
Ryan T. Botts, Ale Jan Homburg, Todd R. Young. The Hopf bifurcation with bounded noise. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2997-3007. doi: 10.3934/dcds.2012.32.2997 |
[2] |
Matteo Franca, Russell Johnson, Victor Muñoz-Villarragut. On the nonautonomous Hopf bifurcation problem. Discrete and Continuous Dynamical Systems - S, 2016, 9 (4) : 1119-1148. doi: 10.3934/dcdss.2016045 |
[3] |
John Guckenheimer, Hinke M. Osinga. The singular limit of a Hopf bifurcation. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 2805-2823. doi: 10.3934/dcds.2012.32.2805 |
[4] |
Kie Van Ivanky Saputra, Lennaert van Veen, Gilles Reinout Willem Quispel. The saddle-node-transcritical bifurcation in a population model with constant rate harvesting. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 233-250. doi: 10.3934/dcdsb.2010.14.233 |
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Russell Johnson, Francesca Mantellini. A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 209-224. doi: 10.3934/dcds.2003.9.209 |
[6] |
Fang Han, Bin Zhen, Ying Du, Yanhong Zheng, Marian Wiercigroch. Global Hopf bifurcation analysis of a six-dimensional FitzHugh-Nagumo neural network with delay by a synchronized scheme. Discrete and Continuous Dynamical Systems - B, 2011, 16 (2) : 457-474. doi: 10.3934/dcdsb.2011.16.457 |
[7] |
Hooton Edward, Balanov Zalman, Krawcewicz Wieslaw, Rachinskii Dmitrii. Sliding Hopf bifurcation in interval systems. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 3545-3566. doi: 10.3934/dcds.2017152 |
[8] |
Qigang Yuan, Jingli Ren. Periodic forcing on degenerate Hopf bifurcation. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2857-2877. doi: 10.3934/dcdsb.2020208 |
[9] |
Rebecca McKay, Theodore Kolokolnikov, Paul Muir. Interface oscillations in reaction-diffusion systems above the Hopf bifurcation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2523-2543. doi: 10.3934/dcdsb.2012.17.2523 |
[10] |
Fernando Antoneli, Ana Paula S. Dias, Rui Paiva. Coupled cell networks: Hopf bifurcation and interior symmetry. Conference Publications, 2011, 2011 (Special) : 71-78. doi: 10.3934/proc.2011.2011.71 |
[11] |
R. Ouifki, M. L. Hbid, O. Arino. Attractiveness and Hopf bifurcation for retarded differential equations. Communications on Pure and Applied Analysis, 2003, 2 (2) : 147-158. doi: 10.3934/cpaa.2003.2.147 |
[12] |
Fatihcan M. Atay. Delayed feedback control near Hopf bifurcation. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 197-205. doi: 10.3934/dcdss.2008.1.197 |
[13] |
Bernold Fiedler. Global Hopf bifurcation in networks with fast feedback cycles. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 177-203. doi: 10.3934/dcdss.2020344 |
[14] |
Begoña Alarcón, Víctor Guíñez, Carlos Gutierrez. Hopf bifurcation at infinity for planar vector fields. Discrete and Continuous Dynamical Systems, 2007, 17 (2) : 247-258. doi: 10.3934/dcds.2007.17.247 |
[15] |
Bing Zeng, Pei Yu. A hierarchical parametric analysis on Hopf bifurcation of an epidemic model. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022069 |
[16] |
Dmitriy Yu. Volkov. The Hopf -- Hopf bifurcation with 2:1 resonance: Periodic solutions and invariant tori. Conference Publications, 2015, 2015 (special) : 1098-1104. doi: 10.3934/proc.2015.1098 |
[17] |
Udhayakumar Kandasamy, Rakkiyappan Rajan. Hopf bifurcation of a fractional-order octonion-valued neural networks with time delays. Discrete and Continuous Dynamical Systems - S, 2020, 13 (9) : 2537-2559. doi: 10.3934/dcdss.2020137 |
[18] |
Qi An, Weihua Jiang. Spatiotemporal attractors generated by the Turing-Hopf bifurcation in a time-delayed reaction-diffusion system. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 487-510. doi: 10.3934/dcdsb.2018183 |
[19] |
Xiaofeng Xu, Junjie Wei. Turing-Hopf bifurcation of a class of modified Leslie-Gower model with diffusion. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 765-783. doi: 10.3934/dcdsb.2018042 |
[20] |
Shu Li, Zhenzhen Li, Binxiang Dai. Stability and Hopf bifurcation in a prey-predator model with memory-based diffusion. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022025 |
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