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.

Global positive periodic solutions of age-dependent competing systems

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.

Interactional models for adults of two populations with maturation delays

This paper is concerned with interactional models for adults of two species delayed by their mature periods. The existence and local stability of equilibria are discussed thoroughly for competitive systems, cooperative systems and predator-prey systems, respectively. For systems with interaction of competition and cooperation, it is found that the two populations are uniformly persistent if the positive equilibrium is stable. For predator-prey interaction, however, some further conditions are needed to guarantee the persistence of the systems.

Existence and uniqueness of solutions for a hierarchical system of two age-structured populations

We propose a class of new hierarchical model for the evolution of two interacting age-structured populations,which is a system of integro-partial differential equations with global feedback boundary conditions and may describe the interactions such as competition,cooperation and predator-prey relation.Based upon a group of natural conditions,the existence and uniqueness of solutions on infinite time interval are proved by means of fixed point and extension principle,and the continuous dependence of the solution on the initial age distribution is established.These results lay a sound basis for the investigation of stability,controllability and variable optimal control problems.

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

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 sizedependent.Existence and uniqueness of nonnegative solutions to the system are analyzed.The 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 technique.Some sufficient conditions for asymptotical stability/instability of steady states are obtained.The resulting conclusion extends some existing results involving age-independent and age-dependent population models.

On exponential stability for systems with state delays

This paper considers the issue of delay-dependent exponential stability for time-delay systems. Both nominal and uncertain systems are investigated. New sufficient conditions in terms of linear matrix inequalities(LMIs) are obtained. These criteria are simple owing to the use of an integral inequality. The model transformation approaches,bounding techniques for cross terms and slack matrices are all avoided in the derivation. Rigorous proof and numerical examples showed that the proposed criteria and those based on introducing slack matrices are equivalent.

Estimation of Semi-Varying Coefficient Model with Surrogate Data and Validation Sampling

In this paper, we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error. With the help of validation sampling, we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption. We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate. Data-driven bandwidth selection methods are also discussed. Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.

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

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.

Supplier pricing based on threshold cointegration in agri-supply chain

Aiming atthe pricing of primary agricultural products for the large-scale suppliers and the wholesalers in agri-supply chain management, an approach for the large-scale supplier pricing is presented based on the threshold cointegration method of wholesale prices online including the GBand-TAR modified Band-TAR model. Our empirical work shows that it is more appropriate for a large-scale supplier pricing with his wholesalers based on the threshold cointegration method than the conventional linear cointegration method in spatially separate markets in an agri-supply chain of soybean in China in short time. Firstly, the three pairs of prices in spatially separate markets are of long-run equilibrium and threshold cointegration. The forecast wst shows that the threshold cointegration approach is superior to the conventional linear cointegration approach in short time. Secondly, there are two thresholds of GBand-TAR in which the threshold parameters represent relative transaction costs. Larger thresholds or wider neutral band corresponds to the greater distance between markets. Thirdly, the estimation of M-TAR shows that the large-scale supplier is more sensitive to increase of wholesaler prices than decrease of wholesaler prices. The supplier can price on the forecast of market price by the threshold ECM including the GBand-TAR if the equilibrium error of threshold lag is not in the interval of thresholds in which there is not profitable trading opportunities for the supplier.

Optimal harvesting of a hierarchical age-struetured population system

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 condition.The 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 result.In addition,some numerical experiments are presented to show the effects of the price function and younger's weight on the optimal profits.

The global dynamics of a discrete nonlinear hierarchical population system

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 members.We 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 systems.Our work demonstrates that the reproductive number governs the evolution of the population.Besides the theoretical results,some numerical experiments are also presented.

Stability for a competing system of hierarchical age-structured populations

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 populations.The age-specified environment is incorporated in the vital rates,which displays the hierarchy of ages.By a non-zero fixed-point result,we show the existence of positive equilibria.Some conditions for the stability of steady states are derived by means of semigroup method.Furthermore,numerical experiments are also presented.

Theory of optimal harvesting for a nonlinear size-structured population in periodic environments

This paper investigates the theoretical aspects for an optimal harvesting problem of a nonlinear size-structured population model in a periodic environment. We establish the well-posedness of the state system by means of frozen coefficients and fixed point reasoning. The existence of a unique optimal policy is proved via Ekeland＇s variational principle, and the first-order optimality conditions are derived by a suitable normM cone and a dual system. The results obtained would be beneficial for exploration of renewable

Theoretical resillts of optimal harvesting in a hierarchical size-structured population system with delay

We investigate an optimal control problem for a hierarchical size-structured populationmodel,which incorporates the inoculation delay into the globally feedbacked boundarycondition.After the establishment of the continuity of the states with respect to theharvesting efforts,the existence of the optimal solutions is proved by a result in convexanalysis,and the maximum principle is obtained via conjugate system and tangent-normal cones.

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

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.