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.

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.

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.

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.

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.

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.

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.

Dynamical study of a predator-prey system with Michaelis-Menten type predator-harvesting

The predation process plays a significant role in advancing life evolution and the maintenance of ecological balance and biodiversity.Hunting cooperation in predators is one of the most remarkable features of the predation process,which benefits the predators by developing fear upon their prey.This study investigates the dynamical behavior of a modified LV-type predator-prey system with Michaelis-Menten-type harvesting of predators where predators adopt cooperation strategy during hunting.The ecologically feasible steady states of the system and their asymptotic stabilities are explored.The local codimension one bifurcations,viz.transcritical,saddle-node and Hopf bifurcations,that emerge in the system are investigated.Sotomayors approach is utilized to show the appearance of transcritical bifurcation and saddle-node bifurcation.A backward Hopfbifurcation is detected when the harvesting effort is increased,which destabilizes the system by generating periodic solutions.The stability nature of the Hopf-bifurcating periodic orbits is determined by computing the first Lyapunov coefficient.Our analyses revealed that above a threshold value of the harvesting effort promotes the coexistence of both populations.Similar periodic solutions of the system are also observed when the conversion efficiency rate or the hunting cooperation rate is increased.We have also explored codimension two bifurcations viz.the generalized Hopf and the Bogdanov-Takens bifurcation exhibit by the system.To visualize the dynamical behavior of the system,numerical simulations are conducted using an ecologically plausible parameter set.The existence of the bionomic equilibrium of the model is analyzed.Moreover,an optimal harvesting policy for the proposed model is derived by considering harvesting effort as a control parameter with the help of Pontryagins maximum principle.

Harvest optimization for sustainable agriculture:The case of tea harvest scheduling

To ensure sustainability in agriculture,many optimization problems need to be solved.An important one of them is harvest scheduling problem.In this study,the harvest scheduling problem for the tea is discussed.The tea harvest problem includes the creating a harvest schedule by considering the farmers'quotas under the purchase location and factory capacity.Tea harvesting is carried out in cooperation with the farmer-factory.Factory man-agement is interested in using its resources.So,the factory capacity,purchase location capacities and number of expeditions should be considered during the harvesting process.When the farmer's side is examined,it is seen that the real professions of farmers are different.On harvest days,farmers often cannot attend to their primary professions.Considering the harvest day preferences of farmers in creating the harvest schedule are of great importance for sustainability in agriculture.Two different mathematical models are proposed to solve this problem.The first model minimizes the number of weekly expeditions of factory vehicles within the factor and purchase location capacity restrictions.The second model minimizes the number of expeditions and aims to comply with the preferences of the farmers as much as possible.A sample application was performed in a region with 12 purchase locations,988 farmers,and 3392 decares of tea fields.The results show that the compli-ance rate of farmers to harvesting preferences could be increased from 52%to 97%,and this situation did not affect the number of expeditions of the factory.This result shows that considering the farmers'preferences on the harvest day will have no negative impact on the factory.On the contrary,it was concluded that this situation increases sustainability and encouragement in agriculture.Furthermore,the results show that models are effective for solving the problem.

一种基于“最优捕集窗口”设计的全球化空气取水系统

Atmospheric water harvesting(AWH)is a promising solution to the water shortage problem.Current sorption-based AWH(SAWH)systems seldom obtain both wide climatic adaptability and high energy efficiency due to the lack of thermodynamic optimization.To achieve the ideal harvesting circulation in SAWH systems,the“optimal harvesting window”(OHW)design based on thermodynamic analysis was first proposed and validated by our prototype.The“OHW”theory indicates the water production rate and energy efficiency could be improved by properly reducing the adsorption temperature.As the humidity increases,the optimal adsorption temperature should be closer to the dew point of the environment.Experimental results revealed that,loaded with 3 kg widely adopted silica gel,the daily water production could reach 5.76-17.64 L/d with ultrahigh energy efficiency of 0.46-1.5 L/kWh.This prototype could also achieve optimal performance in wide climatic conditions in terms of 13-35℃and 18%-72%RH.Lastly,the performance of photovoltaic(PV)-driven SAWH was evaluated.Results showed that a 1 m^(2)PV panel could generate 0.66-2 L water per day in Shanghai throughout the year,the highest in opening literature.Notably,this work introduces a promising concept that can help achieve large-scale,ultra-fast,energyefficient AWH worldwide.

Dynamical behavior of a delayed prey-predator-scavenger system with fear effect and linear harvesting

In this paper,we propose a delayed prey-predator-scavenger system with fear effect and linear harvesting.First,we discuss the existence and stability of all possible equilibria.Next,we investigate the existence of Hopf bifurcation of the delayed system by regarding the gestation period of the scavenger as a bifurcation parameter.Furthermore,we obtain the direction of Hopf bifurcation and the stability of bifurcating periodic solutions by using the normal form theory and the central manifold theorem.In addition,we give the optimal harvesting strategy of the delayed system based on Pontryagin's maximum principle with delay.Finally,some numerical simulations are carried out to verify our theoretical results.

OPTIMAL CONTROL PROBLEM FOR A PERIODIC PREDATOR-PREY MODEL WITH AGE-DEPENDENCE

In this paper,we investigate optimal policy for periodic predator-prey system with age-dependence.Namely,we consider the model with periodic vital rates and initial distribution.The existence of optimal control strategy is discussed by Mazur’s theorem and optimality condition is derived by means of normal cone.

OPTIMAL IMPULSIVE CONTROL IN COMPETITIVE SYSTEM

In this paper, the impulsive exploitation of two species periodic competitive system is considered. First, we show that this type of system with impulsive harvesting has a unique positive periodicsolution, which is globally asymptotically stable. Further, by choosing the maximum total revenues as the management objective, we investigate the optimal harvesting policies for periodic competitive system with impulsive harvesting. Finally, we obtain the optimal time to harvest and optimal population level.

Seasonal Variation,Microscopic and Chromatographic Analysis of Leaves in Malus hupehensis:A Protocol for Its Quality Control

Objective To establish a quality control protocol based on microscopic, TLC, and HPLC methods, and to verify the optimal harvesting time for the leaves of Malus hupehensis(LMH). Methods The LMH were pulverized into powder for microscopic identification or TLC and HPLC analysis after ultrasonic extraction with methanol. Seasonal variations of the phlorizin content and average leaf weight were determined by HPLC analysis and weighing up the leaves collected from May to October. Results Microscopic and macromorphologic characteristics have been described for the leaf identification. A qualitative TLC assay and a quantitative HPLC method have been established for the quality control of LMH. Phlorizin was selected as a reference marker, which resolved at Rf 0.53 in TLC assay and at 14.0 min in HPLC assay. The content of phlorizin decreased gradually from 17.0% in leaves collected in May to 7.5% in October. The average leaf weight reached the level of 0.6 g in August and maintained until its falling.Conclusion These methods are simple, selective, accurate, and reliable for the quality control of LMH. The period from late August to early September is suggested as the optimal harvesting time of the LMH.