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W. M. Getz 《Journal of Optimization Theory and Applications》1979,28(4):585-602
The problem of harvesting two competing populations is formulated in an optimal control setting. The maximum sustained rent (MSR) solution is introduced and is shown to be not only totally singular, but also to play a central role in solutions to the harvesting problem. It is further shown that nonsingular extremal subarcs must in general approach and leave the MSR along partially singular curves. A numerical example is introduced to demonstrate this phenomenon. In the case where the populations are driven onto the MSR in minimum time, however, the optimal control is shown to be bang-bang with at most one switch.The author is indebted to Professor D. H. Jacobson and Dr. D. H. Martin for helpful discussions during the preparation of this paper. 相似文献
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C. Koen 《Journal of Optimization Theory and Applications》1988,58(1):83-91
The aim of the paper is to investigate different types of calculus of variations solutions maximizing the present value of a renewable resource. It is found that there are two types of optimal stationary harvesting policies. For certain cost functions, bang-bang harvesting may be more profitable than either of these. 相似文献
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Dianli Zhao Haidong Liu Yanli Zhou Sanling Yuan 《Journal of Applied Analysis & Computation》2020,10(4):1256-1266
A stochastic population model with the mixed harvesting strategy is formulated and studied in this paper. Sufficient and necessary conditions for survival of the species are derived firstly. Then, based on the ergodic stationary distribution, the optimal strategy is identified. Results show that the linear harvesting effort threatens to the survival of the species; the quadratic harvesting strategy occupies an absolute advantage in the harvesting and excludes the linear part out of the optimal harvesting strategy. It''s interest to see all these occur only in the random environments. Computer simulations are carried out to support the obtained results. 相似文献
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In this paper, we study the global structure of the positive solutions to a logistic equation with constant yield harvesting under Neumann boundary value conditions. Moreover, we show that the logistic equation with the variable coefficients has exactly either zero, or one, or two solutions depending on the harvesting parameter. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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§ 1 Introduction and setting of the problemThe optimal control of age-dependent population dynamics has been intensivelystudied in the last two decades and there is now a vast stock of literature on the topic ofoptimal control problems ofage-structured population dynamics.(see [1 -9] ) .To the bestof our knowledge,the works of Brokate[3,4] are the firstto deal with this topic.Since then,many authors devote to the optimal harvesting problem.In this aspect,we refere to thefundamental papers o… 相似文献
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Q. Zhou 《Journal of Optimization Theory and Applications》1996,88(1):247-249
Recently published results of Gift (Ref. 1) are concerned with the necessary conditions for singular optimal control problems (in the sense of Pontryagin's minimum principle). However, those results are incorrect. An illustrative counterexample is given here.This paper was written while the author studied at Fudan University. The author wishes to thank Professor X. J. Li for his guidance and encouragement. The research was partially supported by NSF of China and the Chinese State Education Commission NSF. 相似文献
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Global asymptotic stability of a two species competitive system with stage structure and harvesting 总被引:3,自引:0,他引:3
Xinyu SONG Lansun CHEN Department of Mathematics Xinyang Teachers College Henan China Institute of Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《Communications in Nonlinear Science & Numerical Simulation》2001,6(2)
Introduction' There have recently appeared in the literature several mathematical models of stagestructured population growth, i. e., models which take into account the faCt that individuals in a population may belong to one of two classes, the immatures and the matureslllZI.Cannibalism has been observed in a great variety of species, including a number of fish species.Cannibalism models of various types have also been investigatedI3"l. In these models, the ageto maturity is represented by a… 相似文献
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Liming Cai Xuezhi Li Jingyuan Yu Guangtian Zhu 《Mathematical Methods in the Applied Sciences》2008,31(7):859-877
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. 相似文献
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S. J. G. Gift 《Journal of Optimization Theory and Applications》1993,76(3):477-484
A new necessary condition for singular optimal control problems is presented in this paper. The condition is simpler to apply than existing conditions and is easily derived from a Taylor series expansion of the performance index. 相似文献
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D. A. Carlson 《Journal of Optimization Theory and Applications》1987,53(2):219-235
In this paper, we extend the existence theory of Brock and Haurie concerning the existence of sporadically catching-up optimal solutions for autonomous, infinite-horizon optimal control problems. This notion of optimality is one of a hierarchy of types of optimality that have appeared in the literature to deal with optimal control problems whose cost functionals, described by an improper integral, either diverge or are unbounded below. Our results rely on the now classical convexity and seminormality hypotheses due to Cesari and are weaker than those assumed in the work of Brock and Haurie. An example is presented where our results are applicable, but those of the above-mentioned authors do not.This research forms part of the author's doctoral dissertation, written at the University of Delaware, Newark, Delaware, under the supervision of Professor T. S. Angell. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(6):1686-1696
In this article bio-economics of a renewable resource that is subjected to strong Allee effect (multiplicative Allee effect) is investigated from sole owner perspective. The considered optimal harvesting problem has been solved using Pontryagin maximum principle. The control problem admits multiple singular equilibrium solutions in contrast to the case where the growth of the resource is of compensatory nature. Thus the choice of optimal singular solution and the nature of associated approach paths make the problem pertinent and interesting. 相似文献
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《中国科学A辑(英文版)》2007,(7)
The double loop network(DLN)is a circulant digraph with n nodes and outdegree 2.It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems.Given the number n of nodes,how to construct a DLN which has minimum diameter?This problem has attracted great attention.A related and longtime unsolved problem is:for any given non-negative integer k,is there an infinite family of k-tight optimal DLN?In this paper,two main results are obtained:(1)for any k≥0,the infinite families of k-tight optimal DLN can be constructed,where the number n(k,e,c)of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c.(2)for any k≥0, an infinite family of singular k-tight optimal DLN can be constructed. 相似文献
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R. Sadigh-esfandiari J. M. Sloss J. C. Bruch Jr 《Journal of Optimization Theory and Applications》1990,66(2):211-226
A maximum principle for the open-loop optimal control of a vibrating system relative to a given convex index of performance is investigated. Though maximum principles have been studied by many people (see, e.g., Refs. 1–5), the principle derived in this paper is of particular use for control problems involving mechanical structures. The state variable satisfies general initial conditions as well as a self-adjoint system of partial differential equations together with a homogeneous system of boundary conditions. The mass matrix is diagonal, constant, and singular, and the viscous damping matrix is diagonal. The maximum principle relates the optimal control with the solution of the homogeneous adjoint equation in which terminal conditions are prescribed in terms of the terminal values of the optimal state variable. An application of this theory to a structural vibrating system is given in a companion paper (Ref. 6). 相似文献
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R. Gabasov F. M. Kirillova N. S. Pavlenok 《Computational Mathematics and Mathematical Physics》2008,48(10):1715-1745
A linear-quadratic optimal control problem subject to geometric constraints on the controls is studied. Techniques for finding the optimal open-loop control and constructing a closed-loop control are described. The problem solution can include special intervals and sections with chattering modes. The proposed techniques make it possible to find special intervals and construct realizable approximations of unrealizable chattering modes to any degree of accuracy. 相似文献
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The double loop network (DLN) is a circulant digraph with n nodes and outdegree 2. It is an important topological structure of computer interconnection networks and has been widely used in the designing of local area networks and distributed systems. Given the number n of nodes, how to construct a DLN which has minimum diameter? This problem has attracted great attention. A related and longtime unsolved problem is: for any given non-negative integer k, is there an infinite family of k-tight optimal DLN? In this paper, two main results are obtained: (1) for any k ≥ 0, the infinite families of k-tight optimal DLN can be constructed, where the number n(k,e,c) of their nodes is a polynomial of degree 2 in e with integral coefficients containing a parameter c. (2) for any k ≥ 0,an infinite family of singular k-tight optimal DLN can be constructed. 相似文献
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王晖 《纯粹数学与应用数学》2013,(5):520-528
研究一类基于比率且具有收获和时滞的捕食系统.证明了系统正周期解的存在性,并通过构造适当的Lyapunov泛函,给出了正周期解全局稳定的充分条件. 相似文献
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Samin T. Malik 《Numerical Functional Analysis & Optimization》2013,34(15):1669-1689
AbstractIn this article, an optimal control problem with a delay in control is considered. The second-order necessary condition is obtained for the optimality of singular (in the sense of the maximum principle) control. Also, the notion of degenerate singular control of order k (k?≥?1) is introduced and for optimality of this, the high-order necessary condition is obtained. Moreover, while studying the problem, one of the strengthened version of an analog of the maximum principle is shown. Finally, the rich content of the obtained results is illustrated by specific examples. 相似文献