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Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets
Admissible wavefront speeds for a single species reaction-diffusion equation with delay
1. | Department of Mathematics II, National Technical University ‘KPI’, Kyiv, United States |
2. | Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca |
[1] |
Zhao-Xing Yang, Guo-Bao Zhang, Ge Tian, Zhaosheng Feng. Stability of non-monotone non-critical traveling waves in discrete reaction-diffusion equations with time delay. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 581-603. doi: 10.3934/dcdss.2017029 |
[2] |
Rui Huang, Ming Mei, Kaijun Zhang, Qifeng Zhang. Asymptotic stability of non-monotone traveling waves for time-delayed nonlocal dispersion equations. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1331-1353. doi: 10.3934/dcds.2016.36.1331 |
[3] |
Ming Mei. Stability of traveling wavefronts for time-delayed reaction-diffusion equations. Conference Publications, 2009, 2009 (Special) : 526-535. doi: 10.3934/proc.2009.2009.526 |
[4] |
Abraham Solar. Stability of non-monotone and backward waves for delay non-local reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5799-5823. doi: 10.3934/dcds.2019255 |
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Yong Jung Kim, Wei-Ming Ni, Masaharu Taniguchi. Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 3707-3718. doi: 10.3934/dcds.2013.33.3707 |
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Yicheng Jiang, Kaijun Zhang. Stability of traveling waves for nonlocal time-delayed reaction-diffusion equations. Kinetic and Related Models, 2018, 11 (5) : 1235-1253. doi: 10.3934/krm.2018048 |
[7] |
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 |
[8] |
Tarik Mohammed Touaoula, Mohammed Nor Frioui, Nikolay Bessonov, Vitaly Volpert. Dynamics of solutions of a reaction-diffusion equation with delayed inhibition. Discrete and Continuous Dynamical Systems - S, 2020, 13 (9) : 2425-2442. doi: 10.3934/dcdss.2020193 |
[9] |
Alfonso Castro, Benjamin Preskill. Existence of solutions for a semilinear wave equation with non-monotone nonlinearity. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 649-658. doi: 10.3934/dcds.2010.28.649 |
[10] |
Wei Wang, Wanbiao Ma. Global dynamics and travelling wave solutions for a class of non-cooperative reaction-diffusion systems with nonlocal infections. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3213-3235. doi: 10.3934/dcdsb.2018242 |
[11] |
Guo Lin, Wan-Tong Li, Mingju Ma. Traveling wave solutions in delayed reaction diffusion systems with applications to multi-species models. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 393-414. doi: 10.3934/dcdsb.2010.13.393 |
[12] |
Tiberiu Harko, Man Kwong Mak. Travelling wave solutions of the reaction-diffusion mathematical model of glioblastoma growth: An Abel equation based approach. Mathematical Biosciences & Engineering, 2015, 12 (1) : 41-69. doi: 10.3934/mbe.2015.12.41 |
[13] |
Weijiu Liu. Asymptotic behavior of solutions of time-delayed Burgers' equation. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 47-56. doi: 10.3934/dcdsb.2002.2.47 |
[14] |
A. Dall'Acqua. Positive solutions for a class of reaction-diffusion systems. Communications on Pure and Applied Analysis, 2003, 2 (1) : 65-76. doi: 10.3934/cpaa.2003.2.65 |
[15] |
Maurizio Garrione, Marta Strani. Monotone wave fronts for $(p, q)$-Laplacian driven reaction-diffusion equations. Discrete and Continuous Dynamical Systems - S, 2019, 12 (1) : 91-103. doi: 10.3934/dcdss.2019006 |
[16] |
Heather Finotti, Suzanne Lenhart, Tuoc Van Phan. Optimal control of advective direction in reaction-diffusion population models. Evolution Equations and Control Theory, 2012, 1 (1) : 81-107. doi: 10.3934/eect.2012.1.81 |
[17] |
Wei Feng, Weihua Ruan, Xin Lu. On existence of wavefront solutions in mixed monotone reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 815-836. doi: 10.3934/dcdsb.2016.21.815 |
[18] |
Rui Li, Yuan Lou. Some monotone properties for solutions to a reaction-diffusion model. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4445-4455. doi: 10.3934/dcdsb.2019126 |
[19] |
Anatoli F. Ivanov, Bernhard Lani-Wayda. Periodic solutions for three-dimensional non-monotone cyclic systems with time delays. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 667-692. doi: 10.3934/dcds.2004.11.667 |
[20] |
Shi-Liang Wu, Tong-Chang Niu, Cheng-Hsiung Hsu. Global asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 3467-3486. doi: 10.3934/dcds.2017147 |
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