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The protection zone of biological population. (English) Zbl 1203.92069
Summary: Many species are endangered, and if we do not act fastly, we are going to lose them forever. Establishing a protection zone is widely used to protect endangered species. How is the effect of this method? What factors affect the effect of the protection zone? We study this topic by a new mathematical model. We examine the effect of the protection zone and conclude that the protection zone is effective for conservation of population resources and ecological environment, though in some cases the extinction cannot be eliminated. The dangerous region, the parameters domains and the typical bifurcation curves of stability of steady states for the considered system are determined. Our results provide theoretical evidence for the practical management of biological resources.
MSC:
92D40Ecology
34C60Qualitative investigation and simulation of models (ODE)
37N25Dynamical systems in biology
References:
[1]Fan, M.; Wang, K.: Study on harvested population with diffusional maigration, Journal of systems science and complexity 14, No. 2 (2001)
[2]Du, Y.; Shi, J.: A diffusive predator–prey model with a protection zone, Journal of differential equations 229, 63-91 (2006) · Zbl 1142.35022 · doi:10.1016/j.jde.2006.01.013
[3]Du, Y.; Liang, X.: A diffusive competition model with a protection zone, Journal of differential equations 244, 61-86 (2008) · Zbl 1138.35039 · doi:10.1016/j.jde.2007.10.005
[4]Du, Y.; Peng, R.; Wang, M.: Effect of a protection zone in the diffusive Leslie predator–prey model, Journal of differential equations 246, 3932-3956 (2009) · Zbl 1168.35444 · doi:10.1016/j.jde.2008.11.007
[5]Ami, D.; Cartigny, P.; Rapaport, A.: Can marine protected areas enhance both economic and biological situations?, Comptes rendus, biologies 328, 357-366 (2005)
[6]Jerry, M.; Rapaport, A.; Cartigny, P.: Can protected areas potentially enlarge viability domains for harvesting management?, Nonlinear analysis RWA 11, 720-734 (2010) · Zbl 1185.91124 · doi:10.1016/j.nonrwa.2009.01.042
[7]Loisel, Patrice: Pierre cartigny, how to model marine reserves?, Nonlinear analysis RWA 10, 1784-1796 (2009) · Zbl 1159.91454 · doi:10.1016/j.nonrwa.2008.02.023