Dynamical behavior of a harvest single species model on growing habitat
Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1357-1368
Printed September 30, 2014
Zhi Ling and Lai Zhang
Yangzhou University, Ume{\aa} University
Abstract : This paper is concerned with a reaction-diffusion single speci\-es model with harvesting on $n$-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The asymptotic behavior of the solution to the problem is obtained by using the method of upper and lower solutions. The results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution, but the effect of the harvesting rate is opposite. The analytical findings are validated with the numerical simulations.
Keywords : growing domain, population model, asymptotic behavior
MSC numbers : 35K57, 92C15
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