Permanence and Stability of an Age-Structured Prey-Predator System with Delays

Cai, Liming; Li, Xuezhi; Song, Xinyu; Yu, Jingyuan

doi:https://doi.org/10.1155/2007/54861

Discrete Dynamics in Nature and Society

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Research Article | Open Access

Volume 2007 | Article ID 054861 | https://doi.org/10.1155/2007/54861

Permanence and Stability of an Age-Structured Prey-Predator System with Delays

Liming Cai,^1,2Xuezhi Li,¹Xinyu Song,¹and Jingyuan Yu²

Received15 Mar 2007

Accepted30 Apr 2007

Published19 Jun 2007

Abstract

An age-structured prey-predator model with delays is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, permanence, and stability are analyzed. By using the persistence theory for infinite-dimensional systems, the sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, sufficient conditions are also obtained for the global asymptotic stability of the positive equilibrium of the model.

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Copyright

Copyright © 2007 Liming Cai et al. 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.

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