Positive periodic solutions and optimal control for a distributed biological model of two interacting species

✍ Scribed by G. Fragnelli; P. Nistri; D. Papini

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 346 KB
• Volume: 12
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2010.10.002

✦ Synopsis

The paper deals with the existence of positive periodic solutions to a system of degenerate parabolic equations with delayed nonlocal terms and Dirichlet boundary conditions. Taking in each equation a meaningful function as a control parameter, we show that for a suitable choice of a class of such controls we have, for each of them, a time-periodic response of the system under different assumptions on the kernels of the nonlocal terms. Finally, we consider the problem of the minimization of a cost functional on the set of pairs: controlperiodic response. The considered system may be regarded as a possible model for the coexistence problem of two biological populations, which dislike crowding and live in a common territory, under different kind of intra-and inter-specific interferences.