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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

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Commun. Math. Biol. Neurosci. 2013 (2013), Article ID 2

Existence and Stability of Solutions for a diffusive Predator-Prey Model with Predator Cannibalism

Yujuan Jiao

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Abstract

In this paper, we consider a diffusive predator-prey modelwith predator cannibalism. Using the energy estimates andGagliardo-Nirenberg-type inequalities, the existence and uniformboundedness of global solutions for the model are proved. Meanwhile,the sufficient conditions for global asymptotic stability of thepositive equilibrium for this model aregiven by constructing a Lyapunov function.

Published
1 July 2013
Volume
2013 (2013)
License
CC BY 3.0

Copyright © 2013 Yujuan Jiao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

Y. Jiao, Existence and Stability of Solutions for a diffusive Predator-Prey Model with Predator Cannibalism, Commun. Math. Biol. Neurosci. 2013 (2013), 2.

BibTeX
@article{Jiao2013,
  author  = {Jiao, Yujuan},
  title   = {Existence and Stability  of Solutions for a diffusive Predator-Prey  Model with  Predator  Cannibalism},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2013},
  year    = {2013},
  pages   = {2},
  doi     = {}
}