Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Spreading speeds and traveling wave solutions in cooperative integral-differential 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 reaction-transport systems, Phys. Rev. Lett., 86 (2001), 926-929.
2 Y. Jin and X. -Q. Zhao, Spatial dynamics of a periodic population model with dispersal, Nonlinearity, 22 (2009), 1167-1189.       
3 M. A. Lewis, B. Li and H. F. Weinberger, Spreading speeds and linear conjecture for two-species competition models, J. Math. Biol., 45 (2002), 219-233.       
4 B. Li, H. F. Weinberger and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196 (2005), 82-98.       
5 B. Li, Traveling wave solutions in partially degenerate cooperative reaction-diffusion systems, J. Diff. Eqs., 252 (2012), 4842-4861.       
6 B. Li and L. Zhang, Travelling wave solutions in delayed cooperative systems, Nonlinearity, 24 (2011), 1759-1776.       
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), 1-40.       
8 X. Liang and X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal., 259 (2010), 857-903.       
9 R. Lui, Biological growth and spread modeled by systems of recursions I. Mathematical theory, Math. Biosci., 93 (1989), 269-295.       
10 F. Lutscher, E. Pachepsky and M. A. Lewis, The effect of dispersal patterns on stream populations, SIAM Rev., 47 (2005), 749-772.       
11 V. Méndez, T. Pujol and J. Fort, Dispersal probability distributions and the wave-front speed problem, Phys. Rev. E., 65 (2002), 041109/1-041109/6.
12 K. Meyer and B. Li, A spatial model of plants with an age-Structured seed bank and juvenile stage, SIAM. J. Appl. Math., 73 (2013), 1676-1702.       
13 J. Medlock and M. Kot, Spreading disease: Integral-differential equations old and new, Math. Biosci., 184 (2003), 201-222.       
14 D. Mollison, Dependence of epidemic and population velocities on basic parameters, Math. Biosci., 107 (1991), 255-287.
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), 814-826.       
17 H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), 183-218.       
18 H. F. Weinberger, M. A. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207-222.       
19 Z.-X. Yu and R. Yuan, Travelling wave solutions in nonlocal reactiondiffusion systems with delays and applications, ANZIAM J., 51 (2009), 49-66.       
20 L. Zhang and B. Li, Traveling waves in an integro-differential competition model, Discrete and Continuous Dynamical Systems-Series B, 17 (2012), 417-428.       

Go to top