Analysis of dynamic properties on forest restoration-population pressure model
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 positiv...
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doaj-3a849a676de04d7f8af01d3062d43bd92021-08-05T00:56:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-05-011743567358110.3934/mbe.2020201Analysis of dynamic properties on forest restoration-population pressure modelMingzhu Qu0Chunrui Zhang1Xingjian Wang 21. Department of Mathematics, Northeast Forestry University, Harbin 150040, China1. Department of Mathematics, Northeast Forestry University, Harbin 150040, China2. College of Information and Computer Engineering, Northeast Forestry University, Harbin 150040, ChinaOn 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.https://www.aimspress.com/article/doi/10.3934/mbe.2020201?viewType=HTMLforest restorationpopulation pressureturing instabilityhopf bifurcationpatterns |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mingzhu Qu Chunrui Zhang Xingjian Wang |
spellingShingle |
Mingzhu Qu Chunrui Zhang Xingjian Wang Analysis of dynamic properties on forest restoration-population pressure model Mathematical Biosciences and Engineering forest restoration population pressure turing instability hopf bifurcation patterns |
author_facet |
Mingzhu Qu Chunrui Zhang Xingjian Wang |
author_sort |
Mingzhu Qu |
title |
Analysis of dynamic properties on forest restoration-population pressure model |
title_short |
Analysis of dynamic properties on forest restoration-population pressure model |
title_full |
Analysis of dynamic properties on forest restoration-population pressure model |
title_fullStr |
Analysis of dynamic properties on forest restoration-population pressure model |
title_full_unstemmed |
Analysis of dynamic properties on forest restoration-population pressure model |
title_sort |
analysis of dynamic properties on forest restoration-population pressure model |
publisher |
AIMS Press |
series |
Mathematical Biosciences and Engineering |
issn |
1551-0018 |
publishDate |
2020-05-01 |
description |
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. |
topic |
forest restoration population pressure turing instability hopf bifurcation patterns |
url |
https://www.aimspress.com/article/doi/10.3934/mbe.2020201?viewType=HTML |
work_keys_str_mv |
AT mingzhuqu analysisofdynamicpropertiesonforestrestorationpopulationpressuremodel AT chunruizhang analysisofdynamicpropertiesonforestrestorationpopulationpressuremodel AT xingjianwang analysisofdynamicpropertiesonforestrestorationpopulationpressuremodel |
_version_ |
1721221628133638144 |