American Institute of Mathematical Sciences

Advanced
February  2009, 25(1): 321-342. doi: 10.3934/dcds.2009.25.321

Homogenization and influence of fragmentation in a biological invasion model

Mohammad El Smaily 1, , François Hamel 2, and  Lionel Roques 3,

1. 

Department of Mathematics, University of British Columbia and Pacific Institute for the Mathematical Sciences, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada
2. 

Aix-Marseille Université, LATP, Faculté des Sciences et Techniques, Avenue Escadrille Normandie-Niemen, F-13397 Marseille Cedex 20
3. 

UR 546 Biostatistique et Processus Spatiaux, INRA, F-84000 Avignon, France

Received  July 2007 Revised  May 2008 Published  June 2009

In this paper, some properties of the minimal speeds of pulsating Fisher-KPP fronts in periodic environments are established. The limit of the speeds at the homogenization limit is proved rigorously. Near this limit, generically, the fronts move faster when the spatial period is enlarged, but the speeds vary only at the second order. The dependence of the speeds on habitat fragmentation is also analyzed in the case of the patch model.
Keywords: Homogenization, pulsating fronts., fragmentation, reaction-diffusion model.
Mathematics Subject Classification: Primary: 35B10, 35B27, 35K57; Secondary: 92B0.
Citation: Mohammad El Smaily, François Hamel, Lionel Roques. Homogenization and influence of fragmentation in a biological invasion model. Discrete & Continuous Dynamical Systems - A, 2009, 25 (1) : 321-342. doi: 10.3934/dcds.2009.25.321
[1]

Michaël Bages, Patrick Martinez. Existence of pulsating waves in a monostable reaction-diffusion system in solid combustion. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 817-869. doi: 10.3934/dcdsb.2010.14.817
[2]

Antoine Mellet, Jean-Michel Roquejoffre, Yannick Sire. Generalized fronts for one-dimensional reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 303-312. doi: 10.3934/dcds.2010.26.303
[3]

Masaharu Taniguchi. Multi-dimensional traveling fronts in bistable reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 1011-1046. doi: 10.3934/dcds.2012.32.1011
[4]

Masaharu Taniguchi. Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3981-3995. doi: 10.3934/dcds.2020126
[5]

Masaharu Taniguchi. Traveling fronts in perturbed multistable reaction-diffusion equations. Conference Publications, 2011, 2011 (Special) : 1368-1377. doi: 10.3934/proc.2011.2011.1368
[6]

Henri Berestycki, Guillemette Chapuisat. Traveling fronts guided by the environment for reaction-diffusion equations. Networks & Heterogeneous Media, 2013, 8 (1) : 79-114. doi: 10.3934/nhm.2013.8.79
[7]

Hakima Bessaih, Yalchin Efendiev, Razvan Florian Maris. Stochastic homogenization for a diffusion-reaction model. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 5403-5429. doi: 10.3934/dcds.2019221
[8]

Keng Deng. On a nonlocal reaction-diffusion population model. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 65-73. doi: 10.3934/dcdsb.2008.9.65
[9]

Zhiting Xu, Yingying Zhao. A reaction-diffusion model of dengue transmission. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2993-3018. doi: 10.3934/dcdsb.2014.19.2993
[10]

Feng-Bin Wang. A periodic reaction-diffusion model with a quiescent stage. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 283-295. doi: 10.3934/dcdsb.2012.17.283
[11]

Wei-Jie Sheng, Wan-Tong Li. Multidimensional stability of time-periodic planar traveling fronts in bistable reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2681-2704. doi: 10.3934/dcds.2017115
[12]

Shi-Liang Wu, Tong-Chang Niu, Cheng-Hsiung Hsu. Global asymptotic stability of pushed traveling fronts for monostable delayed reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3467-3486. doi: 10.3934/dcds.2017147
[13]

Shi-Liang Wu, Yu-Juan Sun, San-Yang Liu. Traveling fronts and entire solutions in partially degenerate reaction-diffusion systems with monostable nonlinearity. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 921-946. doi: 10.3934/dcds.2013.33.921
[14]

Zhi-Xian Yu, Rong Yuan. Traveling wave fronts in reaction-diffusion systems with spatio-temporal delay and applications. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 709-728. doi: 10.3934/dcdsb.2010.13.709
[15]

Maurizio Garrione, Marta Strani. Monotone wave fronts for $(p, q)$-Laplacian driven reaction-diffusion equations. Discrete & Continuous Dynamical Systems - S, 2019, 12 (1) : 91-103. doi: 10.3934/dcdss.2019006
[16]

Alexander Mielke, Sina Reichelt, Marita Thomas. Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion. Networks & Heterogeneous Media, 2014, 9 (2) : 353-382. doi: 10.3934/nhm.2014.9.353
[17]

Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223
[18]

Jia-Feng Cao, Wan-Tong Li, Meng Zhao. On a free boundary problem for a nonlocal reaction-diffusion model. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4117-4139. doi: 10.3934/dcdsb.2018128
[19]

Rui Li, Yuan Lou. Some monotone properties for solutions to a reaction-diffusion model. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 4445-4455. doi: 10.3934/dcdsb.2019126
[20]

Keng Deng, Yixiang Wu. Asymptotic behavior for a reaction-diffusion population model with delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 385-395. doi: 10.3934/dcdsb.2015.20.385

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (51)
  • HTML views (0)
  • Cited by (21)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences