A ratio‐dependent predator–prey model with stage structure and optimal harvesting policy |
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| Authors: | Liming Cai Xuezhi Li Jingyuan Yu Guangtian Zhu |
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| Institution: | 1. Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, People's Republic of China;2. Beijing Institute of Information Control, Beijing 100037, China;3. Academy of Mathematics and System Science, C.A.S., Beijing 100080, China |
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| Abstract: | In this paper, a ratio‐dependent predator–prey model with stage structure and harvesting is investigated. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence and stability are performed. By constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. The existence possibilities of bioeconomic equilibria have been examined. An optimal harvesting policy is also given by using Pontryagin's maximal principle. Copyright © 2007 John Wiley & Sons, Ltd. |
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| Keywords: | predator– prey system stage structure ratio dependence global stability optimal harvesting policy |
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