Analysis of dynamic properties on forest restoration-population pressure model

• Main Authors: Mingzhu Qu, Chunrui Zhang, Xingjian Wang
• Format: Article
• Language: English
• Published: AIMS Press 2020-05-01
• Series: Mathematical Biosciences and Engineering
• Subjects: forest restoration; population pressure; turing instability; hopf bifurcation; patterns
• Online Access: https://www.aimspress.com/article/doi/10.3934/mbe.2020201?viewType=HTML

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.