Dynamics of the predator-prey models on the two-patch fragmented habitat with dispersal

Authors

  • Ting-Hui Yang
  • Kaijen Cheng
  • Jin-Wei Yu

DOI:

https://doi.org/10.5556/j.tkjm.47.2016.1984

Abstract

In this work, we consider the population-dispersal dynamics for predator-prey interactions in a two-patch environment. On each fragmented patch, there is a two-species predator-prey ecological system. It is assumed that the predator species are mobile. The existence and local dynamics of boundary equilibria and interior equilibria with respect to parameters are completely classified. Moreover, global extinction results are established analytically. In particular, the phenomenon of over-exploitation is also found in these discrete patches models. Finally, some biological interpretations are discussed.

Author Biography

Ting-Hui Yang

Department ofMathematics, Tamkang University, Tamsui, New Taipei City 25137, Taiwan.

References

R.Cressman and V.Krivan, Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds, Journal of Mathematical Biology, 67(2013), 329--358.

D.L. DeAngelis, G.S.K. Wolkowicz, Y.Lou, Y.Jiang, M.Novak, R.Svanback, M.S. Araujo, Y.Jo and E.A. Cleary, The effect of travel loss on evolutionarily stable distributions of populations in space,The American naturalist, 178(2011), 15--29.

R. Levins, Evolution in Changing Environments. Princeton University Press, Princeton, 1969.

Y. Lou and C.-H. Wu, Global dynamics of a tritrophic model for two patches with cost of dispersal, SIAM Journal on Applied Mathematics, 71(2011),1801--1820.

L. Markus, Asymptotically autonomous differential systems, In Contributions to the theory of nonlinear oscillations, vol. 3, 17--29. Princeton University Press, Princeton, N. J., 1956.

M.L. McKinney, Urbanization, Biodiversity, and Conservation The impacts of urbanization on native species are poorly studied, but educating a highly urbanized human population about these impacts can greatly improve species conservation in all ecosystems,BioScience, 52(2002), 883--890.

T.Namba, A.Umemoto and E.Minami, The effects of habitat fragmentation on persistence of source-sink metapopulations in systems with predators and prey or apparent competitors, Theoretical Population Biology,56(1999), 123-137.

M.R. W. Rands, W.M. Adams, L.Bennun, S.H.M. Butchart, A.Clements, D.Coomes, A.Entwistle, I.Hodge, V.Kapos, J.P.W. Scharlemann, W.J. Sutherland and B.Vira. Biodiversity Conservation: Challenges Beyond 2010, Science (New York, NY), 329 (201), 1298--1303.

S.P.D. Riley, R. M. Sauvajot, T.K. Fuller, E.C. York, D.A. Kamradt, C.Bromley and R.K. Wayne, Effects of Urbanization and Habitat Fragmentation on Bobcats and Coyotes in Southern California, Conservation Biology, 17(2003), 566--576.

G.A.K. van Voorn, L.Hemerik, M.P. Boer and B.W. Kooi, Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect,

Mathematical Biosciences,209(2007), 451--469.

J.Wang, J.Shi and J.Wei. Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey, J Differential Equations, 251 (2011), 1276--1304.

J.Wang, J.Shi and J.Wei, Predator-prey system with strong Allee effect in prey. Journal of Mathematical Biology, 62(2011), 291--331.

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Published

2016-03-30

How to Cite

Yang, T.-H., Cheng, K., & Yu, J.-W. (2016). Dynamics of the predator-prey models on the two-patch fragmented habitat with dispersal. Tamkang Journal of Mathematics, 47(1). https://doi.org/10.5556/j.tkjm.47.2016.1984

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