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Density of hyperbolicity and homoclinic bifurcations for attracting topologically hyperbolic sets
Admissible wavefront speeds for a single species reactiondiffusion 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] 
ZhaoXing Yang, GuoBao Zhang, Ge Tian, Zhaosheng Feng. Stability of nonmonotone noncritical traveling waves in discrete reactiondiffusion equations with time delay. Discrete and Continuous Dynamical Systems  S, 2017, 10 (3) : 581603. doi: 10.3934/dcdss.2017029 
[2] 
Rui Huang, Ming Mei, Kaijun Zhang, Qifeng Zhang. Asymptotic stability of nonmonotone traveling waves for timedelayed nonlocal dispersion equations. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 13311353. doi: 10.3934/dcds.2016.36.1331 
[3] 
Ming Mei. Stability of traveling wavefronts for timedelayed reactiondiffusion equations. Conference Publications, 2009, 2009 (Special) : 526535. doi: 10.3934/proc.2009.2009.526 
[4] 
Abraham Solar. Stability of nonmonotone and backward waves for delay nonlocal reactiondiffusion equations. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 57995823. doi: 10.3934/dcds.2019255 
[5] 
Yong Jung Kim, WeiMing Ni, Masaharu Taniguchi. Nonexistence of localized travelling waves with nonzero speed in single reactiondiffusion equations. Discrete and Continuous Dynamical Systems, 2013, 33 (8) : 37073718. doi: 10.3934/dcds.2013.33.3707 
[6] 
Yicheng Jiang, Kaijun Zhang. Stability of traveling waves for nonlocal timedelayed reactiondiffusion equations. Kinetic and Related Models, 2018, 11 (5) : 12351253. doi: 10.3934/krm.2018048 
[7] 
Qi An, Weihua Jiang. Spatiotemporal attractors generated by the TuringHopf bifurcation in a timedelayed reactiondiffusion system. Discrete and Continuous Dynamical Systems  B, 2019, 24 (2) : 487510. doi: 10.3934/dcdsb.2018183 
[8] 
Tarik Mohammed Touaoula, Mohammed Nor Frioui, Nikolay Bessonov, Vitaly Volpert. Dynamics of solutions of a reactiondiffusion equation with delayed inhibition. Discrete and Continuous Dynamical Systems  S, 2020, 13 (9) : 24252442. doi: 10.3934/dcdss.2020193 
[9] 
Alfonso Castro, Benjamin Preskill. Existence of solutions for a semilinear wave equation with nonmonotone nonlinearity. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 649658. doi: 10.3934/dcds.2010.28.649 
[10] 
Wei Wang, Wanbiao Ma. Global dynamics and travelling wave solutions for a class of noncooperative reactiondiffusion systems with nonlocal infections. Discrete and Continuous Dynamical Systems  B, 2018, 23 (8) : 32133235. doi: 10.3934/dcdsb.2018242 
[11] 
Guo Lin, WanTong Li, Mingju Ma. Traveling wave solutions in delayed reaction diffusion systems with applications to multispecies models. Discrete and Continuous Dynamical Systems  B, 2010, 13 (2) : 393414. doi: 10.3934/dcdsb.2010.13.393 
[12] 
Tiberiu Harko, Man Kwong Mak. Travelling wave solutions of the reactiondiffusion mathematical model of glioblastoma growth: An Abel equation based approach. Mathematical Biosciences & Engineering, 2015, 12 (1) : 4169. doi: 10.3934/mbe.2015.12.41 
[13] 
Weijiu Liu. Asymptotic behavior of solutions of timedelayed Burgers' equation. Discrete and Continuous Dynamical Systems  B, 2002, 2 (1) : 4756. doi: 10.3934/dcdsb.2002.2.47 
[14] 
A. Dall'Acqua. Positive solutions for a class of reactiondiffusion systems. Communications on Pure and Applied Analysis, 2003, 2 (1) : 6576. doi: 10.3934/cpaa.2003.2.65 
[15] 
Maurizio Garrione, Marta Strani. Monotone wave fronts for $(p, q)$Laplacian driven reactiondiffusion equations. Discrete and Continuous Dynamical Systems  S, 2019, 12 (1) : 91103. doi: 10.3934/dcdss.2019006 
[16] 
Heather Finotti, Suzanne Lenhart, Tuoc Van Phan. Optimal control of advective direction in reactiondiffusion population models. Evolution Equations and Control Theory, 2012, 1 (1) : 81107. doi: 10.3934/eect.2012.1.81 
[17] 
Wei Feng, Weihua Ruan, Xin Lu. On existence of wavefront solutions in mixed monotone reactiondiffusion systems. Discrete and Continuous Dynamical Systems  B, 2016, 21 (3) : 815836. doi: 10.3934/dcdsb.2016.21.815 
[18] 
Rui Li, Yuan Lou. Some monotone properties for solutions to a reactiondiffusion model. Discrete and Continuous Dynamical Systems  B, 2019, 24 (8) : 44454455. doi: 10.3934/dcdsb.2019126 
[19] 
Anatoli F. Ivanov, Bernhard LaniWayda. Periodic solutions for threedimensional nonmonotone cyclic systems with time delays. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 667692. doi: 10.3934/dcds.2004.11.667 
[20] 
ShiLiang Wu, TongChang Niu, ChengHsiung Hsu. Global asymptotic stability of pushed traveling fronts for monostable delayed reactiondiffusion equations. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 34673486. doi: 10.3934/dcds.2017147 
2020 Impact Factor: 1.392
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