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Diffusive Holling type-II predator-prey system with harvesting of prey

Shabani, S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jmaa.2013.08.055
  3. Abstract:
  4. We study diffusive heterogeneous predator-prey system with Holling type-II functional response in the presence of harvesting in prey equation i.e.{-δu=λu-a(x)u2-buv1+mu-ch(x)in Ω,-δv=μv-v2+duv1+muin Ω,∂νu=∂νv=0on ∂Ω, where Ω is a smooth bounded region in RN and a(x) is a nonnegative continuous function on Ω, with Ω0 a region such that Ω⊂Ω and a(x)>0 on Ω\u03a90. We show that in the case of weak prey growth rate, i.e. λ less than the first eigenvalue of -δ in Ω0, the system has a positive solution for the values of μ in a bounded interval and c>0 sufficiently small. We also investigate the multiplicity of positive solutions in this case. When the prey growth rate is strong, we will show that the system has a positive solution for large positive value of μ, again provided that c is sufficiently small
  5. Keywords:
  6. Bifurcation ; Degree theory ; Harvesting ; Predator-prey system
  7. Source: Journal of Mathematical Analysis and Applications ; Vol. 410, issue. 1 , 2014 , pp. 469-482 ; ISSN: 0022247X
  8. URL: http://www.sciencedirect.com/science/article/pii/S0022247X13007993