-
Previous Article
Bifurcation of a heterodimensional cycle with weak inclination flip
- DCDS-B Home
- This Issue
-
Next Article
A constructive proof of the existence of a semi-conjugacy for a one dimensional map
Global stability and convergence rate of traveling waves for a nonlocal model in periodic media
1. | School of Mathematics and Physics, University of South China, Hengyang, 421001, China |
2. | Department of Mathematics and Statistics, Memorial University of Newfoundland, St.Johns, Newfoundland, A1C 5S7, Canada |
References:
[1] |
N. F. Britton, "Reaction-diffusion Equations and their Applications to Biology,'' Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1986. |
[2] |
P. C. Fife, "Mathematical Aspect of Reacting and Diffusing Systems,'' Lecture Notes in Biomath., 28, Springer-Verlag, Berlin-New York, 1979. |
[3] |
P. C. Fife and J. B. Mcleod, The approach solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361.
doi: 10.1007/BF00250432. |
[4] |
A. Friedman, "Partial Differential Equations of Parabolic Type,'' Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. |
[5] |
S. A. Gourley and Y. Kuang, Wavefront and global stability in a time-delayed population model with stage structure, R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 459 (2003), 1563-1579.
doi: 10.1098/rspa.2002.1094. |
[6] |
A. N. Kolmogorov, I. G. Petrowsky and N. S. Piscounov, Étude de l'équation de la diffusion avec croissance de la quantité de matiére et son application á un probléme biologique, Bull. Univ. d'État á Moscou, Ser. Internat. A, 1 (1937), 1-26. |
[7] |
M. Mei, C.-K. Lin, C.-T. Lin and J. W.-H. So, Traveling wavefronts for time-delayed reaction-diffusion equation. I. Local nonlinearity, J. Differential Equations, 247 (2009), 495-510.
doi: 10.1016/j.jde.2008.12.026. |
[8] |
M. Mei, C.-K. Lin, C.-T. Lin and J. W.-H. So, Traveling wavefronts for time-delayed reaction-diffusion equation. II. Nonlocal nonlinearity, J. Differential Equations, 247 (2009), 511-529.
doi: 10.1016/j.jde.2008.12.020. |
[9] |
M. Mei and J. W.-H. So, Stability of strong travelling waves for a non-local time-delayed reaction-diffusion equation, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 551-568. |
[10] |
M. Mei, C. Ou and X.-Q. Zhao, Global stability of monostable traveling waves for nonlocal time-delayed reaction-diffusion equations, SIAM J. Math. Anal., 42 (2010), 2762-2790.
doi: 10.1137/090776342. |
[11] |
J. D. Murry, "Mathematical Biology,'' Vols. I and II, Springer-Verlag, New York, 2002. |
[12] |
A. N. Stokes, On two types of moving front in quasilinear diffusion, Math. Biosci., 31 (1976), 307-315.
doi: 10.1016/0025-5564(76)90087-0. |
[13] |
V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskki and G. Yakhno, "Autowave Processes in Kinetic Systems,'' Reidel, Dorgrecht, 1987. |
[14] |
P. Weng and X.-Q. Zhao, Spatial dynamics of a nonlocal and delayed population model in a periodic habitat, Discrete and Continuous Dynamical Systems Ser. A, 29 (2011), 343-366.
doi: 10.3934/dcds.2011.29.343. |
show all references
References:
[1] |
N. F. Britton, "Reaction-diffusion Equations and their Applications to Biology,'' Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1986. |
[2] |
P. C. Fife, "Mathematical Aspect of Reacting and Diffusing Systems,'' Lecture Notes in Biomath., 28, Springer-Verlag, Berlin-New York, 1979. |
[3] |
P. C. Fife and J. B. Mcleod, The approach solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361.
doi: 10.1007/BF00250432. |
[4] |
A. Friedman, "Partial Differential Equations of Parabolic Type,'' Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. |
[5] |
S. A. Gourley and Y. Kuang, Wavefront and global stability in a time-delayed population model with stage structure, R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 459 (2003), 1563-1579.
doi: 10.1098/rspa.2002.1094. |
[6] |
A. N. Kolmogorov, I. G. Petrowsky and N. S. Piscounov, Étude de l'équation de la diffusion avec croissance de la quantité de matiére et son application á un probléme biologique, Bull. Univ. d'État á Moscou, Ser. Internat. A, 1 (1937), 1-26. |
[7] |
M. Mei, C.-K. Lin, C.-T. Lin and J. W.-H. So, Traveling wavefronts for time-delayed reaction-diffusion equation. I. Local nonlinearity, J. Differential Equations, 247 (2009), 495-510.
doi: 10.1016/j.jde.2008.12.026. |
[8] |
M. Mei, C.-K. Lin, C.-T. Lin and J. W.-H. So, Traveling wavefronts for time-delayed reaction-diffusion equation. II. Nonlocal nonlinearity, J. Differential Equations, 247 (2009), 511-529.
doi: 10.1016/j.jde.2008.12.020. |
[9] |
M. Mei and J. W.-H. So, Stability of strong travelling waves for a non-local time-delayed reaction-diffusion equation, Proc. Roy. Soc. Edinburgh Sect. A, 138 (2008), 551-568. |
[10] |
M. Mei, C. Ou and X.-Q. Zhao, Global stability of monostable traveling waves for nonlocal time-delayed reaction-diffusion equations, SIAM J. Math. Anal., 42 (2010), 2762-2790.
doi: 10.1137/090776342. |
[11] |
J. D. Murry, "Mathematical Biology,'' Vols. I and II, Springer-Verlag, New York, 2002. |
[12] |
A. N. Stokes, On two types of moving front in quasilinear diffusion, Math. Biosci., 31 (1976), 307-315.
doi: 10.1016/0025-5564(76)90087-0. |
[13] |
V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskki and G. Yakhno, "Autowave Processes in Kinetic Systems,'' Reidel, Dorgrecht, 1987. |
[14] |
P. Weng and X.-Q. Zhao, Spatial dynamics of a nonlocal and delayed population model in a periodic habitat, Discrete and Continuous Dynamical Systems Ser. A, 29 (2011), 343-366.
doi: 10.3934/dcds.2011.29.343. |
[1] |
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 |
[2] |
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 |
[3] |
Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, 2021, 29 (4) : 2599-2618. doi: 10.3934/era.2021003 |
[4] |
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 |
[5] |
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 |
[6] |
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 |
[7] |
Wei-Jie Sheng, Wan-Tong Li. Multidimensional stability of time-periodic planar traveling fronts in bistable reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2681-2704. doi: 10.3934/dcds.2017115 |
[8] |
Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1757-1774. doi: 10.3934/dcdsb.2020001 |
[9] |
Zhaosheng Feng. Traveling waves to a reaction-diffusion equation. Conference Publications, 2007, 2007 (Special) : 382-390. doi: 10.3934/proc.2007.2007.382 |
[10] |
Xiaojie Hou, Wei Feng. Traveling waves and their stability in a coupled reaction diffusion system. Communications on Pure and Applied Analysis, 2011, 10 (1) : 141-160. doi: 10.3934/cpaa.2011.10.141 |
[11] |
Ning Wang, Zhi-Cheng Wang. Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay. Discrete and Continuous Dynamical Systems, 2022, 42 (4) : 1599-1646. doi: 10.3934/dcds.2021166 |
[12] |
Bang-Sheng Han, Zhi-Cheng Wang. Traveling wave solutions in a nonlocal reaction-diffusion population model. Communications on Pure and Applied Analysis, 2016, 15 (3) : 1057-1076. doi: 10.3934/cpaa.2016.15.1057 |
[13] |
Masaharu Taniguchi. Instability of planar traveling waves in bistable reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2003, 3 (1) : 21-44. doi: 10.3934/dcdsb.2003.3.21 |
[14] |
Tianran Zhang. Traveling waves for a reaction-diffusion model with a cyclic structure. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1859-1870. doi: 10.3934/dcdsb.2020006 |
[15] |
Xiongxiong Bao, Wan-Tong Li. Existence and stability of generalized transition waves for time-dependent reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3621-3641. doi: 10.3934/dcdsb.2020249 |
[16] |
Matthieu Alfaro, Jérôme Coville, Gaël Raoul. Bistable travelling waves for nonlocal reaction diffusion equations. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1775-1791. doi: 10.3934/dcds.2014.34.1775 |
[17] |
Xiaojie Hou, Yi Li. Local stability of traveling-wave solutions of nonlinear reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 681-701. doi: 10.3934/dcds.2006.15.681 |
[18] |
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 |
[19] |
Shi-Liang Wu, Wan-Tong Li, San-Yang Liu. Exponential stability of traveling fronts in monostable reaction-advection-diffusion equations with non-local delay. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 347-366. doi: 10.3934/dcdsb.2012.17.347 |
[20] |
Guangying Lv, Jinlong Wei, Guang-an Zou. Noise and stability in reaction-diffusion equations. Mathematical Control and Related Fields, 2022, 12 (1) : 147-168. doi: 10.3934/mcrf.2021005 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]