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Forced waves and their asymptotics in a Lotka–Volterra cooperative model under climate change

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  • Yang, Yong
  • Wu, Chufen
  • Li, Zunxian

Abstract

The existence and asymptotics of forced traveling wave front in a Lotka–Volterra cooperative system under climate change are concerned in this paper. By constructing appropriate upper and lower solutions combined with the monotone iteration scheme, we show that for any given positive speed of the shifting habitat edge, there exists a nondecreasing wave front with the speed consistent with the habitat shifting speed, which indicates that no matter how moderate of the habitat shifts, two species will still be driven to extinction as the mutualistic effects exist but weak. Numerical simulations are also given to illustrate our results.

Suggested Citation

  • Yang, Yong & Wu, Chufen & Li, Zunxian, 2019. "Forced waves and their asymptotics in a Lotka–Volterra cooperative model under climate change," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 254-264.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:254-264
    DOI: 10.1016/j.amc.2019.01.058
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    1. Guy F. Midgley & William J. Bond, 2015. "Future of African terrestrial biodiversity and ecosystems under anthropogenic climate change," Nature Climate Change, Nature, vol. 5(9), pages 823-829, September.
    2. John Harte & Annette Ostling & Jessica L. Green & Ann Kinzig, 2004. "Climate change and extinction risk," Nature, Nature, vol. 430(6995), pages 34-34, July.
    3. R. Warren & J. Price & J. VanDerWal & S. Cornelius & H. Sohl, 2018. "The implications of the United Nations Paris Agreement on climate change for globally significant biodiversity areas," Climatic Change, Springer, vol. 147(3), pages 395-409, April.
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