具有尺度结构和双加权的种群模型:稳定性与最优收获

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A Weighted Population Model with Size-Structure: Stability and Optimal Harvesting

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Abstract:

This paper is concerned with the stability and optimal harvesting for a size-structured population model with control of newborns, where fertility and mortality depend the density in different ways. A formal equilibrium is derived and existence of unique steady state is shown via a contraction mapping. Some conditions for asymptotical stability and instability are presented by means of characteristic equation. As for the optimal harvesting problem, we cite the tangent-normal cones to establish an optimal feedback policy, and employ the Ekeland's variational principle to prove the existence and uniqueness of optimal strategies. Two examples demonstrate the evolution of the species.

Key words: Size-structure, Population model, Stability, Optimal control, Normal cone, Ekeland's variational principle

CLC Number:

O211.4

He Zerong, Yang Lizhi. A Weighted Population Model with Size-Structure: Stability and Optimal Harvesting[J].Acta mathematica scientia,Series A, 2016, 36(3): 584-600.

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