Spatiotemporal Dynamics in a Generalized Diffusive Population System of Natural Pinus Koraiensis with Time Delay

Abstract

In this paper, we establish a generalized population system of natural pinus koraiensis with lactation delay and diffusion term. Firstly, through the eigenvalue analysis, the conditions for local asymptotic stability of the positive equilibrium are derived, and the time delay is taken as bifurcation parameter, the existence conditions of Hopf bifurcation are discussed. Secondly, the model is analyzed qualitatively from the bifurcation point of view. The existence conditions of Turing bifurcation are given. By utilizing the normal form and center manifold theories of partial functional differential equations, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are studied, and the related formulae are determined. Finally, a nonlinear population model of pinus koraiensis with time delay and diffusion term is established. The corresponding numerical simulations are performed to verify the effects of time delay and diffusion on the stability of system, and the biological explanation is given.

Keywords

Population of pinus koraiensis / lactation delay / diffusion term / bifurcation / stability