Spreading speeds and traveling wave solutions in cooperative integraldifferential systems
Pages: 1663  1684,
Issue 6,
August
2015
doi:10.3934/dcdsb.2015.20.1663 Abstract
References
Full text (562.8K)
Related Articles
Changbing Hu  Department of Mathematics, University of Louisville, Louisville, KY 40292, United States (email)
Yang Kuang  School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281, United States (email)
Bingtuan Li  Department of Mathematics, University of Louisville, Louisville, KY 40292, United States (email)
Hao Liu  School of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States (email)
1 
S. Fedotov, Front propagation into an unstable state of reactiontransport systems, Phys. Rev. Lett., 86 (2001), 926929. 

2 
Y. Jin and X. Q. Zhao, Spatial dynamics of a periodic population model with dispersal, Nonlinearity, 22 (2009), 11671189. 

3 
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speeds and linear conjecture for twospecies competition models, J. Math. Biol., 45 (2002), 219233. 

4 
B. Li, H. F. Weinberger and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196 (2005), 8298. 

5 
B. Li, Traveling wave solutions in partially degenerate cooperative reactiondiffusion systems, J. Diff. Eqs., 252 (2012), 48424861. 

6 
B. Li and L. Zhang, Travelling wave solutions in delayed cooperative systems, Nonlinearity, 24 (2011), 17591776. 

7 
X. Liang and X.Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Commun. Pure Appl. Math., 60 (2007), 140. 

8 
X. Liang and X.Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal., 259 (2010), 857903. 

9 
R. Lui, Biological growth and spread modeled by systems of recursions I. Mathematical theory, Math. Biosci., 93 (1989), 269295. 

10 
F. Lutscher, E. Pachepsky and M. A. Lewis, The effect of dispersal patterns on stream populations, SIAM Rev., 47 (2005), 749772. 

11 
V. MÃ©ndez, T. Pujol and J. Fort, Dispersal probability distributions and the wavefront speed problem, Phys. Rev. E., 65 (2002), 041109/1041109/6. 

12 
K. Meyer and B. Li, A spatial model of plants with an ageStructured seed bank and juvenile stage, SIAM. J. Appl. Math., 73 (2013), 16761702. 

13 
J. Medlock and M. Kot, Spreading disease: Integraldifferential equations old and new, Math. Biosci., 184 (2003), 201222. 

14 
D. Mollison, Dependence of epidemic and population velocities on basic parameters, Math. Biosci., 107 (1991), 255287. 

15 
S. Pan and G. Lin, Invasion traveling wave solutions of a competitive system with dispersal, Bound. Value Probl., 2012 (2012), 11pp. 

16 
Y.J. Sun, W.T. Li and Z.C. Wang, Traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity, Nonlinear Anal., 74 (2011), 814826. 

17 
H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), 183218. 

18 
H. F. Weinberger, M. A. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207222. 

19 
Z.X. Yu and R. Yuan, Travelling wave solutions in nonlocal reactiondiffusion systems with delays and applications, ANZIAM J., 51 (2009), 4966. 

20 
L. Zhang and B. Li, Traveling waves in an integrodifferential competition model, Discrete and Continuous Dynamical SystemsSeries B, 17 (2012), 417428. 

Go to top
