OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.

Effects of Seed Maturity of Turf-Type Tall Fescue on the Seed Vigor and the Optimal Harvesting Time

By assay of accelerated aging germination, germination index, vigor index, seedling length, seedling weight, electric conductivity, dehydrogenase activity, ATP content and acid phosphoesterase activity during seed development of turf-type tall fescue, the seed vigor of tall fescue were studied. Combining with seed moisture content and yield, the optimal harvesting time of tall fescue was determined. The results indicated that the seed vigor increased continuously along with seed maturity, and the higher seed vigor was achieved at 19th day after perk anthesis and maintained continuously until 31st day after peak anthesis. At 25th day after peak anthesis, the highest yield of 3 533 kg ha-1 and the good quality of seeds of tall fescue were harvested with 32.19% moisture content. From 22nd to 31st day after peak anthesis, the seed yield of 3 300 kg ha-1 and the good quality seeds of tall fescue were harvested with 40 - 12. 43% moisture content, and the span was the optimal harvesting time.

OPTIMAL HARVESTING CONTROL PROBLEM FOR LINEAR AGE-DEPENDENT POPULATION DYNAMICS

An optimal harvesting problem for linear age-dependent population dynamics is investigated.By Mazur's Theorem,the existence of solutions of the optimal control problem (OH) is demonstrated.The first order necessary conditions of optimality for problem (OH) is obtained by the conception of normal cone. Finally,under suitable assumptions,the uniqueness of solutions of the optimal control problem (OH) is given.The results extend some known criteria.

On the optimal harvesting of size-structured population dynamics

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

Growth Dynamics and Optimal Harvesting Stage of Two Forage Maize Varieties

SAUMZ 1 and SAUMZ 2 are two forage maize varieties reproduced by distant hybridization.In a randomized block experiment,their fresh forage yield and dry matter yield were investigated on the basis of growth period,leaf stage,and effective accumulated temperature.The nutritional components were measured in a near infrared diffuse reflectance spectroscopy.Referring to the concept of forage grading index,a formula was constructed to calculate the total digestible energy.The investigated characters and indexes were adapted to suitable models of growth dynamics.The results showed that these two varieties have strong heterosis in fresh forage yield,dry matter yield,and total digestible energy.Their growth dynamics were adapted to Logistic models described by general equation y=k/（1＋ae-bx）.The forage grading indexes of these two varieties were decreased linearly along with the increasing of their leaf stage.The stopping point of fast growing period of total digestible energy estimated on the basis of leaf stage was suggested to be used as optimal harvesting stage of forage maize.The optimal harvesting stage was estimated to be tasseling stage for SAUMZ 1 and 19.50-leaf stage for SAUMZ 2.

OPTIMAL HARVESTING AND STABILITY FOR FISHING MODELS WITH STAGE STRUCTURE IN INSHORE-OFFSHORE AREAS

A fishing model with stage structure in inshore and offshore areas is considered.Steady states of the dynamical system representing fishery are derived and their local,as well as global,stability is discussed.The optimal harvest policy is formulated and solved as an optimal control problem.A numerical example is given to illustrate the solution procedure.

Impulse controls in optimal harvesting of age-structured populations

A nonlinear optimal control problem in the Lotka-McKendrick population model is studied.It describes rational management of age-structured farmed populations in aquaculture and indoor farms.Employing generalized functions,we prove the impulse nature of optimal harvesting.Exact analytic solutions for sustainable harvesting strategies are obtained and used to analyze the optimal dynamics of harvesting age and rotation under technological innovations.

Optimal harvesting of a fuzzy water hyacinth-fish model with Kuznets curve effect

In this paper,we consider the effects of environmental perturbations such as the variations of temperature and climate on the growth of water hyacinth and fish species,as well as the economic and application values of these two species.We first present a triangular fuzzy water hyacinth-fish ecological model with Kuznets curve effect and linear harvesting.Then,we discuss the existence of the equilibria and their stability.It is then followed by analyzing the existence of bionomic equilibrium and determining the optimal harvesting policy via Pontryagin's Maximum Principle.Finally,numerical simulations are performed to validate the theoretical results.Our research indicates that fuzzy parameters may affect the optimal harvesting strategy.

COMPLEXITY ANALYSIS AND COMPUTATION OF THE OPTIMAL HARVESTING FOR ONE-SPECIES POPULATION RESOURCES

The exploitation of renewable resources creates many complex problems for culture, ecology and economics as well. Ascertaining the essentials behind the coraplex problems is very important, in this paper, we mainly study various complex relations appearing in the optimal exploitation process for renewable resources. First, we derive a sufficient condition on the existence of optimal harvesting policies for one-species population resources. Then we present every possible optimal harvesting pattern for such a modeh On the basis of this, we give a computing formula for estimating the optimal harvesting period, optimal transitional period, and optimal recruitment period. The main difference with respect to the previous works in literature is that our optimal harvesting policy is a piece-wise continuous function of time t, at the piecewise point to, which is called switching time. At the switching time we switch the harvesting rate from h to some transitional control u,, then to 0. Clearly this kind of harvesting policy is easier to carry out than those by others, provided that there exists a managing department which can highly supervise the resources.

OPTIMAL HARVESTING POLICY AND STABILITY FOR SINGLE-SPECIES GROWTH MODEL WITH STAGE STRUCTURE

Abstract. In this paper, we consider a stage structure population model with two lifestages, immature and mature, with harvesting mature population and stocking immaturepopulation. It is shown that under suitable hypotheses there exists a globally asymptoti-cally stable positive equilibrium. The effect of the delay on the populations at equilibriumand the optimal harvesting policy for mature population are also considered.

New Development in Study of the Faustmann Optimal Forest Harvesting

Chinese forest resources have become very scarce in the face of rapid economic growth demand, while the reform of collective forest right system is in full swing across the country. It will directly affect the regeneration level of forest resources and the diverse ecological value functions. In this article, the mainstream model paradigm of forest economics, that is, the basic framework of the Faustmann model and its evolution process are made in a more detailed explanation, especially the extended model including considered silvicultural effort, tax subsidies, risk dynamic management, and forest regeneration factors are made in more detailed explanations. This article concludes with the future further research directions of forest economics, including the design of dynamic models that includes considered uneven-aged forest management, non-timber goods and services, dynamic forest models. The research reflects the general trend of interdisciplinary and cross-border.

Optimal harvesting of a prey-predator model with variable carrying capacity

This work deals with a prey-predator model in an environment where the carrying capacities are assumed to be variable with time and one species feeds upon the other. Independent harvesting efforts are applied in either species and asymmetrical intraguild predation occurs. A common resource is consumed by two competing species and at the same time predator also consumes the prey. At first we discuss the model under constant carrying capacity and make the conclusion that no limit cycle exists in this case. Then we discuss the model without intraspecific competition. Our main concern is to cover the above mentioned two cases together, i.e. the model with variable carrying capacity and intraspecific competition. We determine the steady states and examine the dynamical behavior. We also analyze the local and global stability of the interior equilibrium by Routh-Hurwitz criterion and a suitable Lyapunov function respectively. A Hopf bifur- cation occurs with respect to a parameter which is the ratio of predator＇s and prey＇s intrinsic growth rate. The possibility of bionomic equilibrium has been considered. The optimal harvest policy is formulated and solved with Pontryagin＇s maximum principle. Some numerical simulations are given to explain most of the analytical results.

An integrated project of fish and broiler： SIS model with optimal harvesting

The paper analyzes the influence of a susceptible-infectious-susceptible （SIS） infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which the growth rates of both species vary with available nutrients and environmental carrying capacities of biomasses. The nutrients for both species are functions of the biomasses of the two species. The harvesting rates of fish and broiler depend linearly on common effort function. It is assumed that the diseases are trans- mitted to the susceptible populations by direct contact with the infected populations. Using the medicine, some portion of the infected populations are transmitted to the sus- ceptible populations. The existence of steady states and their stability are investigated analytically. The joint profit of the SIS model is maximized using Pontryagin＇s max- imum principle and corresponding optimum harvesting rates are also obtained. Using Mathematica software~ the models are illustrated and the optimum results are obtained and presented in tabular and graphical forms.

OPTIMAL DYNAMICAL BALANCE HARVESTING FOR A CLASS OF RENEWABLE RESOURCES SYSTEM

An optimal utilization problem for a class of renewable resources system is investigated. Firstly, a control problem was proposed by introducing a new utility function which depends on the harvesting effort and the stock of resources.Secondly, the existence of optimal solution for the problem was discussed. Then, using a maximum principle for infinite horizon problem, a nonlinear four-dimensional differential equations system was attained. After a detailed analysis of the unique positive equilibrium solution, the existence of limit cycles for the system is demonstrated. Next a reduced system on the central manifold is carefully derived, which assures the stability of limit cycles. Finally significance of the results in bioeconomics is explained.

The Harvesting Optimal Problem of Richards Model

In this paper, the exploitation of single population modelled by Richards model is studied. By choosing the maximum annual-sustainable yield as management objective, we investigate the optimal harvesting policies for autonomous and periodic exploited Richards model. Further, when the functions in the exploited Richards model are stably bounded functions, we study the ultimately optimal harvesting policy and obtain the corresponding average limiting maximum sustainable yield.

Optimal harvesting strategy and stability analysis of a delay-induced prey-predator system with stage structure

A stage-structured prey-predator model with time delay and harvesting is considered.Some novel sufficient conditions for the local stability of the positive equilibria are obtained by Routh-Hurwitz criteria.Moreover,the existence of a Hopf bifurcation at the coexistence equilibrium is established.Finally,the optimal harvesting problem is formulated and solved by Pontryagin’s maximum principle,and an example is given for illustration.

Optimal Harvesting and Stability for a Predator-prey System with Stage Structure

The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.

Prey-predator model with functional response for optimal harvesting incorporating prey refuge

This paper presents a prey-predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey predator system parameter.

OVERTAKING OPTIMAL HARVESTING FOR AN AGE-DEPENDENT n-DIMENSIONAL FOOD CHAIN MODEL

This paper is concerned with an optimal harvesting problem over an infinite horizon for age-dependent n-dimensional food chain model and the analysis of long-term behaviors of the optimal-controlled system. The existence of overtaking optimal policy is proved and a maximum principle is carefully derived by means of Dubovitskii-Milyutin functional analytical extremum theory. Weak and strong turnpike properties of optimal trajectories are established.

Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization

Converting ambient vibration energy into electrical energy by using piezoelectric energy harvester has attracted a lot of interest in the past few years.In this paper,a topology optimization based method is applied to simultaneously determine the optimal layout of the piezoelectric energy harvesting devices and the optimal position of the mass loading.The objective function is to maximize the energy harvesting performance over a range of vibration frequencies.Pseudo excitation method （PEM） is adopted to analyze structural stationary random responses,and sensitivity analysis is then performed by using the adjoint method.Numerical examples are presented to demonstrate the validity of the proposed approach.