Asymptotic behavior of solutions for a Lotka–Volterra mutualism reaction–diffusion system with time delays

✍ Scribed by Yuan-Ming Wang

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 624 KB
• Volume: 58
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2009.03.094

✦ Synopsis

This paper is to investigate the asymptotic behavior of solutions for a time-delayed Lotka-Volterra N-species mutualism reaction-diffusion system with homogeneous Neumann boundary condition. It is shown, under a simple condition on the reaction rates, that the system has a unique bounded time-dependent solution and a unique constant positive steady-state solution, and for any nontrivial nonnegative initial function the corresponding time-dependent solution converges to the constant positive steadystate solution as time tends to infinity. This convergence result implies that the trivial steady-state solution and all forms of semitrivial steady-state solutions are unstable, and moreover, the system has no nonconstant positive steady-state solution. A condition ensuring the convergence of the time-dependent solution to one of nonnegative semitrivial steady-state solutions is also given.