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A ratio‐dependent predator–prey model with stage structure and optimal harvesting policy
Author(s) -
Cai Liming,
Li Xuezhi,
Yu Jingyuan,
Zhu Guangtian
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.956
Subject(s) - mathematics , verifiable secret sharing , pontryagin's minimum principle , stability (learning theory) , maximum principle , exponential stability , lyapunov function , mathematical economics , predation , set (abstract data type) , control theory (sociology) , mathematical optimization , optimal control , nonlinear system , ecology , economics , computer science , physics , control (management) , management , quantum mechanics , machine learning , programming language , biology
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.