Asymptotic limits of the principal spectrum point of a nonlocal dispersal cooperative system and application to a two-stage structured population model

TL;DR

This paper investigates the asymptotic behavior of the principal spectrum point in nonlocal dispersal cooperative systems, providing insights into how dispersal rates influence system stability and population dynamics.

Contribution

It offers new theoretical results on the limits of the principal spectrum point as dispersal rates vary, and applies these findings to a two-stage structured population model.

Findings

Sign of the principal spectrum point determined for small dispersal rates.

Asymptotic profiles of steady states characterized for large dispersal rates.

Biological implications of dispersal effects discussed.

Abstract

This work examines the limits of the principal spectrum point, $\lambda_p$, of a nonlocal dispersal cooperative system with respect to the dispersal rates. In particular, we provide precise information on the sign of $\lambda_p$ as one of the dispersal rates is : (i) small while the other dispersal rate is arbitrary, and (ii) large while the other is either also large or fixed. We then apply our results to study the effects of dispersal rates on a two-stage structured nonlocal dispersal population model whose linearized system at the trivial solution results in a nonlocal dispersal cooperative system. The asymptotic profiles of the steady-state solutions with respect to the dispersal rates of the two-stage nonlocal dispersal population model are also obtained. Some biological interpretations of our results are discussed.