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Differential Equations and Dynamical Systems

, Volume 27, Issue 1–3, pp 249–276 | Cite as

Another Mechanism to Control Invasive Species and Population Explosion: “Ecological” Damping Continued

  • Rana D. Parshad
  • Guangming Yao
  • Wen LiEmail author
Original Research

Abstract

The control of nonnative species is a central problem in spatial ecology. Data on the invasive Burmese python (Python bivittatus) in the Florida everglades, show an exponential increase in python population, which have resulted in local prey populations reducing severely (Dorcas et al. in Proc Natl Acad Sci 109:2418–2422, 2012). This is exacerbated by the inability to harvest pythons by law, in Everglades National Park, where their concentration is extremely high. We consider a two species predator–prey model with Beddington–DeAngelis functional response, and show that it blows up in finite time, thus mimicking an “exploding” python population. Given current government policy that requires complete protection of species in national parks, we investigate novel alternative population control measures that promote efficient eco-system engineering. We establish such measures are feasible in our setting by rigorously proving boundary damping effects. That is we show that an exploding population in a region can be controlled, solely via manipulation of the boundary, such as effective corridor design. Detailed numerical simulations are performed to justify our analytical results.

Keywords

Predator prey model Finite time blow-up Radial basis function Mixed boundary conditions 

Mathematics Subject Classification

Primary 35B44 35K57 65M70 Secondary 92D25 

Notes

Acknowledgements

We would like to acknowledge valuable comments from the referees that helped us greatly improve the overall quality of the manuscript.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2017

Authors and Affiliations

  1. 1.Department of MathematicsClarkson UniversityPotsdamUSA
  2. 2.College of Big Data ScienceTaiyuan University of TechnologyTaiyuanChina

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