Article

Zeitschrift für angewandte Mathematik und Physik

, Volume 58, Issue 4, pp 571-591

First online:

Traveling fronts in diffusive and cooperative Lotka–Volterra system with nonlocal delays

  • Wan-Tong LiAffiliated withSchool of Mathematics and Statistics, Lanzhou University Email author 
  • , Zhi-Cheng WangAffiliated withSchool of Mathematics and Statistics, Lanzhou UniversityDepartment of Mathematics, Hexi University

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Abstract.

This paper is concerned with a diffusive and cooperative Lotka–Volterra model with distributed delays and nonlocal spatial effect. By using an iterative technique recently developed by Wang, Li and Ruan (Traveling wave fronts in reaction-diffusion systems with spatio-temporal delays, J. Differential Equations 222 (2006), 185–232), sufficient conditions are established for the existence of traveling wave front solutions connecting the zero and the positive equilibria by choosing different kernels. The result is an extension of an existing result for Fisher-KPP equation with nonlocal delay and is somewhat parallel to the existing result for diffusive and cooperative Lotka–Volterra system with discrete delays.

Mathematics Subject Classification (2000).

35K57 34K10 35B20

Keywords.

Traveling wave fronts Lotka–Volterra system iterative technique nonlocal delays