Research ArticlesNo Access

The effect of diffusion loss on the time-varying giant Panda population

Meng Zhang

College of Forestry, Beijing Forestry University, Beijing 100083, P. R. China

School of Science, Beijing University of Civil Engineering, and Architecture, Beijing 100044, P. R. China

Search for more papers by this author

and

Guohua Song

Canvard College, Beijing Technology and Business University, Beijing 101118, P. R. China

E-mail Address: songguohua@bucea.edu.cn

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S1793524516500625Cited by:3 (Source: Crossref)

Abstract

It has been certificated that corridors can help giant pandas to keep their habitat from fragmenting. However there are still losses during the process of moving along corridors. In this study, a mathematical model with Allee effect is carried out to describe the diffusion of giant pandas between n patches. Some criteria are obtained to keep the system persisting. It is proved that the system has a unique positive $ω$ -periodic solution which is globally asymptotically stable. The ecological meanings of these findings are discussed following the results. And some numerical simulations in the Qinling Mountain giant panda nature reservation area are also presented in the end.

Keywords:

AMSC: 03C90

Remember to check out the Most Cited Articles in IJB!

Check out new Biomathematics books in our Mathematics 2018 catalogue!
Featuring author Frederic Y M Wan and more!

References

1. M. F. Allison and D. B. Robert, A framework for the design of wildlife conservation corridors with specific application to southwestern Ontario, Landscape Urban Plan. 37 (1997) 163–186. Crossref, Web of Science, Google Scholar
2. F. Courchamp, L. Berec and J. Gascoigne, Allee Effect in Ecology and Conservation (Oxford University Press, Oxford, 2008). Crossref, Google Scholar
3. J. A. Cui and Y. Takeuchi, Permanence of a single-species dispersal system and predator survival, J. Comput. Appl. Math. 175 (2005) 375–394. Crossref, Web of Science, Google Scholar
4. X. L. Jin, Present techniques and ex-situ conservation of giant panda in Qinling Mountain, J. Northwest Univ. 38(2) (2008). Google Scholar
5. M. A. Krasnoselskii, The Operator of Translation Along Trajectories of Differential Equations, Translations of Mathematical Monographs, Vol. 19 (American Mathematical Society, Providence, RI, 1968). Google Scholar
6. E. Kuno, Mathematical models for predator–prey interaction, Adv. Ecol. Res. 16 (1987) 252–261. Google Scholar
7. J. Q. Li and G. Z. Shen, The Habitat of Giant Pandas (Higher Education Press, 2012). Google Scholar
8. C. J. Loucks, Z. Lu, E. Dinerstein, D. J. Wang, D. Fa and H. Wang, The giant pandas of the Qinling Mountains, China: A case study in designing conservation landscapes for elevational migrants, Conserv. Biol. 17 (2003) 558–565. Crossref, Web of Science, Google Scholar
9. Z. Y. Lu and Y. C. Zhou, Advances in Mathematical Biology (Scientific Press, 2006). Google Scholar
10. X. Y. Shi, G. H. Song and Z. Y. Li, The effect of diffusion on giant pandas that live in complex patchy environments, Nonlinear Anal. Model. Control 20(1) (2015) 56–71. Crossref, Web of Science, Google Scholar
11. H. L. Smith, Cooperative system of differential equations with concave nonlinearities, Nonlinear Anal. 10 (1986) 1037–1052. Crossref, Web of Science, Google Scholar
12. H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, Vol. 41 (American Mathematical Society, Providence, RI, 1995). Google Scholar
13. G. H. Song and Z. J. Gui, Periodic solutions of a forest-bamboo-giant panda nonlinear dynamic model, J. Beijing Univ. Civil Engrg. Architec. 29(2) (2013) 60–63. Google Scholar
14. State Forestry Administration, The 3rd National Survey Report on Giant Panda in China (Science Publishing House, 2006). Google Scholar
15. C. Q. Sun, Z. L. Zhang and X. L. Jin, The division of Qinlin giant panda local population and number distribution, Wildlife Mag. 26(6) (2005) 51–54. Google Scholar
16. W. H. Xu, Z. Y. Ouyang and A. Vina, Designing a conservation plan for protecting the habitat for giant pandas in the Qionglai Mountain range, Divers. Distrib. 12(5) (2006) 610–619. Crossref, Web of Science, Google Scholar
17. X. Q. Zhao, The qualitative analysis of $N$ -species Lotka–Volterra periodic competition systems, Math. Comput. Model. 15 (1991) 3–8. Crossref, Web of Science, Google Scholar