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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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References

1. R. Brown, J. Agee, J. F. Franklin, Forest restoration and fire: principles in the context of place, Conserv. Biol., 18 (2004), 903-912.

2. C. Ravenscroft, R. Scheller, D. Mladenoff, M. A. White, Forest restoration in a mixed-ownership landscape under climate change, Ecol. Appl., 20 (2010), 327-346.

3. H. Bateman, D. Merritt, J. Johnson, Riparian forest restoration: Conflicting goals, trade-offs, and measures of success, Sustainability, 4 (2012), 2334-2347.

4. S. Peng, Y. Hou, B. Chen, Establishment of Markov successional model and its application for forest restoration reference in Southern China, Ecol. Modell., 221 (2010), 1317-1324.

5. T. Aide, J. Cavelier, Barriers to lowland tropical forest restoration in the Sierra Nevada de Santa Marta, Colombia, Restor. Ecol., 2 (1994), 219-229.

6. R. Chazdon, Tropical forest recovery: Legacies of human impact and natural disturbances, Perspect. Plant Ecol. Evol. Syst., 6 (2003), 51-71.

7. A. Okubo, Diffusion and Ecological Problems: Mathematical Models, Springer Verlag, New York, (1980).

8. C. Zhang, A. Ke, B. Zheng, Patterns of interaction of coupled reaction-diffusion systems of the FitzHugh-Nagumo type, Nonlinear Dyn., 97 (2019), 1451-1476.

9. K. Jesse, Modelling of a diffusive Lotka-Volterra-System: The climate-induced shifting of tundra and forest realms in North-America, Ecol. Modell., 123 (1999), 53-64.

10. Y. Svirezhev, Lotka-Volterra models and the global vegetation pattern, Ecol. Modell., 135 (2000), 135-146.

11. M. Acevedo, M. Marcano M, R. Fletcher, A diffusive logistic growth model to describe forest recovery, Ecol. Modell., 244 (2012), 13-19.

12. E. Holmes, M. Lewis, J. Banks, R. R. Veit, Partial differential equations in ecology: Spatial interactions and population dynamics, Ecology, 75 (1994), 17-29.

13. P. Vitousek, Beyond global warming: Ecology and global change, Ecology, 75 (1994), 1861-1876.

14. C. Nunes, J. Auge, Land-use and Land-cover Change (LUCC): Implementation Strategy, International Geosphere-Biosphere Programme, Environmental Policy Collection, 1999.

15. T. Houet, P. Verburg, T. Loveland, Monitoring and modelling landscape dynamics, Landscape Ecol., 25 (2010), 163-167.

16. H. Pereira, P. Leadley, V. ${\rm{Proen}}\mathop {\rm{c}}\limits_ \cdot {\rm{a}}$, R. Alkemade, J. P. W. Scharlemann, J. F. Fernandez-Manjarres, et al., Scenarios for global biodiversity in the 21st century, Science, 330 (2010), 1496-1501.

17. T. Chase, R. Pielke, T. Kittel, R. R. Nemani, S. W. Running, Simulated impacts of historical land cover changes on global climate in northern winter, Clim. Dyn., 16 (2000), 93-105.

18. R. Houghton, J. Hackler, K. Lawrence, The US carbon budget: contributions from land-use change, Science, 285 (1999), 574-578.

19. E. Lambin, B. Turner, H. Geist, S. B.Agbola, A. Angelsen, J. W. Brucee, et al., The causes of land-use and land-cover change: Moving beyond the myths, Global Environ. Change, 11 (2001), 261-269.

20. R. Chazdon, M. Guariguata, Natural regeneration as a tool for large-scale forest restoration in the tropics: Prospects and challenges, Biotropica, 48 (2016), 716-730.

21. T. Crk, M. Uriarte, F. Corsi, D. Flynn, Forest recovery in a tropical landscape: What is the relative importance of biophysical, socioeconomic, and landscape variables?, Landscape Ecol., 24 (2009), 629-642.

22. J. Chinea, Tropical forest succession on abandoned farms in the Humacao Municipality of eastern Puerto Rico, For. Ecol. Manage., 167 (2002), 195-207.

23. C. Chien, M. Chen, Multiple bifurcations in a reaction-diffusion problem, Comput. Math. Appl., 35 (1998), 15-39.

24. W. Jiang, H. Wang, X. Cao, Turing instability and Turing-Hopf bifurcation in diffusive Schnakenberg systems with gene expression time delay, J. Dyn. Differ. Equations, 31 (2019), 2223-2247.

25. R. Fisher, The wave of advance of advantageous genes, Ann. Hum. Genet., 7 (1937), 355-369.

26. Z. Ju, Y. Shao, W. Kong, X. Ma, X. Fang, An impulsive prey-predator system with stage-structure and Holling II functional response, Adv. Differ. Equations, 2014 (2014), 280.

27. S. Madec, J. Casas, G. Barles, C. Suppo, Bistability induced by generalist natural enemies can reverse pest invasions, J. Math. Biol., 75 (2017), 543-575.

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