In this paper, a singular phytoplankton-zooplankton model with fuzzy parameters, refuge, fishery protection and harvesting is studied by regarding the imprecise biological parameters as one form of triangular fuzzy nu...
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In this paper, a singular phytoplankton-zooplankton model with fuzzy parameters, refuge, fishery protection and harvesting is studied by regarding the imprecise biological parameters as one form of triangular fuzzy number. By using the utility function method, the transformed differential equation is reduced to a differential equation. In absence of economic profit, the existence of positive equilibria, local stability and global stability for the interior equilibrium of the present differential system are discussed, the conditions of Hopf bifurcation occurring at the positive equilibrium are given, and the corresponding nonlinear feedback controller is designed to eliminate Hopf bifurcation. In presence of economic profit, the corresponding differential algebraic model is proposed and some conditions of the existence of the interior equilibrium are derived. By regarding economic profit as bifurcation parameter, singular induced bifurcation occurring is investigated, and a linear controller is designed to remove such bifurcation. Furthermore, Pontryagin's maximum principle has been used to obtain optimal harvesting policy to maximize the benefit as well as conservation of the ecosystem. Finally, some numerical simulations are given to demonstrate our theoretical results after each part. Results show that imprecise parameters not only affect the interior equilibrium and the bionomic equilibrium of system, but also affect the critical value of bifurcation and branch range.
In order to solve the problems of subjectivity and inconsistent of judging matrix, which are encountered in the effectiveness evaluation process of traditional Analytic Hierarchy Process(AHP) method for integrated avi...
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ISBN:
(纸本)9781784660468
In order to solve the problems of subjectivity and inconsistent of judging matrix, which are encountered in the effectiveness evaluation process of traditional Analytic Hierarchy Process(AHP) method for integrated avionics system, an effectiveness evaluation algorithm of integrated avionics system based on improved AHP method is proposed. The algorithm constructs judgment matrix to reduce the expert's subjectivity by using group AHP method and quasi-optimum consistent matrix to solve the inconsistent problem of judging matrix by using least square principle. Then, the bottom indicators are divided into nonquantifiable indicators which obtain the evaluation vector by using experts evaluation method and quantifiable indicators which obtain the evaluation vector by using the utility function method and grey AHP method. Finally, the effectiveness of integrated avionics system is calculated by the evaluation vector and the indicator weight of each layer. The results show that the proposed algorithm can obtain the evaluation result more objective and scientific. It has certain reference value for effectiveness evaluation of integrated avionics system.
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