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Analysis of dynamic properties on forest restoration-population pressure model

1 Department of Mathematics, Northeast Forestry University, Harbin 150040, China
2 College of Information and Computer Engineering, Northeast Forestry University, Harbin 150040, China

Special Issues: Recent Progress in Structured Population Dynamics

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.
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Keywords forest restoration; population pressure; Turing instability; Hopf bifurcation; patterns

Citation: Mingzhu Qu, Chunrui Zhang, Xingjian Wang. Analysis of dynamic properties on forest restoration-population pressure model. Mathematical Biosciences and Engineering, 2020, 17(4): 3567-3581. doi: 10.3934/mbe.2020201

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