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On the optimal harvesting of size-structured population dynamics

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Applied Mathematics(A Journal of Chinese Universities) 2013年第2期28卷 173-186页

作者： LIU Yan CHENG Xiao-liang HE Ze-rong Department of mathematics Zhejiang University institute of operational research and cybernetics Hangzhou Dianzi University

This work is concerned with a kind of optimal control problem for a size-structured biological population ***-posedness of the state system and an adjoint system are proved by means of Banach＇s fixed point *** and uniqueness of optimal control are shown by functional analytical *** conditions describing the optimal strategy are established via tangent and normal cones *** results are of the first ones for this novel structure.

关键词： Body size population model optimal harvest maximum principle normal cone.

Minimizing makespan in a two-stage hybrid flow shop scheduling problem with open shop in one stage

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Applied Mathematics(A Journal of Chinese Universities) 2013年第3期28卷 358-368页

作者： DONG Jian-ming HU Jue-liang CHEN Yong Department of Mathematics Zhejiang Sci-Tech University institute of operational research and cybernetics Hangzhou Dianzi University

This paper considers a scheduling problem in two-stage hybrid flow shop, where the first stage consists of two machines formed an open shop and the other stage has only one machine. The objective is to minimize the makespan, i.e., the maximum completion time of all jobs. We first show the problem is NP-hard in the strong sense, then we present two heuristics to solve the problem. Computational experiments show that the combined algorithm of the two heuristics performs well on randomly generated problem instances.

关键词： hybrid flow shop open shop Heuristic algorithm.

The global dynamics of a discrete nonlinear hierarchical population system

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International Journal of Biomathematics 2019年第2期12卷 217-237页

作者： Ze-Rong He Huai Chen Shu-Ping Wang institute of operational research and cybernetics Hangzhou Dianzi University Hangzhou 310018P.R.China

This paper is concerned with the global dynamics of a hierarchical population model,in which the fertility of an individual depends on the total number of higher-ranking *** investigate the stability of equilibria,nonexistence of periodic orbits and the persistence of the population by means of eigenvalues,Lyapunov function,and several results in discrete dynamical *** work demonstrates that the reproductive number governs the evolution of the *** the theoretical results,some numerical experiments are also presented.

关键词： Dominance rank global stability regeneration number persistence discrete systems

Optimal harvesting of a hierarchical age-struetured population system

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International Journal of Biomathematics 2019年第8期12卷 165-189页

作者： Ze-Rong He Dongdong Ni Shu-Ping Wang institute of operational research and cybernetics Hangzhou Dianzi University Hangzhou 310018P.R.China

We investigate an optimal harvesting problem for age-structured species,in which elder individuals are more competitive than younger ones,and the population is modeled by a highly nonlinear integro-partial differential equation with a global feedback boundary *** existence of optimal strategies is established by means of compactness and maximizing sequences,and the maximum principle obtained via an adjoint system,tangent-normal cones and a new continuity *** addition,some numerical experiments are presented to show the effects of the price function and younger's weight on the optimal profits.

关键词： Dominance rank population system existence maximum principle numerical method

Stability for a competing system of hierarchical age-structured populations

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International Journal of Biomathematics 2020年第7期13卷 325-345页

作者： Ze-Rong He Nan Zhou institute of operational research and Cybernetics Hangzhou Dianzi University Hangzhou 310018P.R.China

In this paper,we are concerned with the stability for a model in the form of system of integro-partial differential equations,which governs the evolution of two competing age-structured *** age-specified environment is incorporated in the vital rates,which displays the hierarchy of *** a non-zero fixed-point result,we show the existence of positive *** conditions for the stability of steady states are derived by means of semigroup ***,numerical experiments are also presented.

关键词： Dominance rank population system equilibria stability semigroup of linear operators

Stability analysis for a size-structured model of species in a space-limited habitat

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International Journal of Biomathematics 2016年第6期9卷 241-262页

作者： Ze-Rong He Qiang-Jun Xie Hai-Tao Wang institute of operational research and cybernetics Hangzhou Dianzi University Hangzhou 310018 P. R. China

We investigate the stability of steady states of a size- and stage-structured population model, which is a hybrid system of ordinary and partial differential equations with global integral feedbacks. After the formulation of a criterion by spectrum method, we derive conditions for global stability of the trivial state and local stability of the positive equilibrium via the basic reproduction rate. Furthermore, some examples and simulations ure .presented to illustrate the obtained results.

关键词： Space-limitation size-dependence spectrum reproduction number stability.

Multi-Stage Voltage Control Optimization Strategy for Distribution Networks Considering Active-Reactive Co-Regulation of Electric Vehicles

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Energy Engineering 2025年第1期122卷 221-242页

作者： Shukang Lyu Fei Zeng Huachun Han HuiyuMiao Yi Pan Xiaodong Yuan Electric Power research institute State Grid Jiangsu Electric Power Co.Ltd.Nanjing211103China

The high proportion of uncertain distributed power sources and the access to large-scale random electric vehicle(EV)charging resources further aggravate the voltage fluctuation of the distribution network,and the existing research has not deeply explored the EV active-reactive synergistic regulating characteristics,and failed to realize themulti-timescale synergistic control with other regulatingmeans,For this reason,this paper proposes amultilevel linkage coordinated optimization strategy to reduce the voltage deviation of the distribution ***,a capacitor bank reactive power compensation voltage control model and a distributed photovoltaic(PV)activereactive power regulationmodel are ***,an external characteristicmodel of EVactive-reactive power regulation is developed considering the four-quadrant operational characteristics of the *** optimization model of the distribution network is then constructed considering the time-series coupling constraints of multiple types of voltage regulators.A multi-timescale control strategy is proposed by considering the impact of voltage regulators on active-reactive EV energy consumption and PV energy ***,a four-stage voltage control optimization strategy is proposed for various types of voltage regulators with multiple time ***-objective optimization is solved with the improvedDrosophila algorithmto realize the power fluctuation control of the distribution network and themulti-stage voltage control *** results validate that the proposed voltage control optimization strategy achieves the coordinated control of decentralized voltage control resources in the distribution *** effectively reduces the voltage deviation of the distribution network while ensuring the energy demand of EV users and enhancing the stability and economic efficiency of the distribution network.

关键词： Electric vehicle(EV) distribution network multi-stage optimization active-reactive power regulation voltage control

Global positive periodic solutions of age-dependent competing systems

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Applied Mathematics(A Journal of Chinese Universities) 2011年第1期26卷 38-46页

作者： HE Ze-rong LIU Li-li LUO Zhi-xue institute of operational research and cybernetics Hangzhou Dianzi University Hangzhou 310018 China Department of Mathematics Lanzhou Jiaotong University Lanzhou 730070 China

This paper is to investigate positive periodic solutions of a biological system composed of two competing species. The existence and uniqueness of nonnegative solutions to the model for a set of given vital rates and initial distribution are treated and the contractive property of the solutions explored. Based on these results, some simple conditions for the global existence of positive periodic orbits are established by means of Horn＇s asymptotic fixed point theorem.

关键词： Population dynamics age-structure Poincare mapping fixed point.

Stability results for a nonlinear two-species competition model with size-structure

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Applied Mathematics(A Journal of Chinese Universities) 2021年第1期36卷 1-15页

作者： LIU Yan HE Ze-rong Department of Mathematics China Jiliang UniversityHangzhou 310018China institute of operational research and cybernetics Hangzhou Dianzi UniversityHangzhou 310018China.

We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community,in which the mortality,fertility and growth are *** and uniqueness of nonnegative solutions to the system are *** existence of the stationary size distributions is discussed,and the linear stability is investigated by means of the semigroup theory of operators and the characteristic equation *** sufficient conditions for asymptotical stability/instability of steady states are *** resulting conclusion extends some existing results involving age-independent and age-dependent population models.

关键词： competition size-structure existence and uniqueness semigroup stability.