Open AccessAnalysis of dynamic properties on forest restoration-population pressure model
Author(s) -
Ming Qu,
Chunrui Zhang,
Xing Jian Wang
Publication year - 2020
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2020201
Subject(s) - hopf bifurcation , mathematics , bifurcation , population , reaction–diffusion system , steady state (chemistry) , population model , square (algebra) , boundary (topology) , instability , bifurcation theory , mathematical analysis , physics , mechanics , geometry , chemistry , demography , nonlinear system , quantum mechanics , sociology
On the basis of logistic models of forest restoration, we consider the influence of population pressure on forest restoration and establish a reaction diffusion model with Holling Ⅱ functional responses. We study this reaction diffusion model under Dirichlet boundary conditions and obtain a positive equilibrium. In the square region, we analyze the existence of Turing instability and Hopf bifurcation near this point. The square patterns and mixed patterns are obtained when steady-state bifurcation occurs, the hyperhexagonal patterns appears in Hopf bifurcation.