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 hypo...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.展开更多
This paper deals with fishing models with stage structure and harvest in an inshore-offshore area. By using the monotonic theory and concave operators to functional differential equations and the qualitative theory of...This paper deals with fishing models with stage structure and harvest in an inshore-offshore area. By using the monotonic theory and concave operators to functional differential equations and the qualitative theory of differential equations, steady states of this dynamical systems representing fishery are derived, and their globally attracting behaviors are discussed. A brief biological meaning for the mathematical results is given.展开更多
A convex two-stage non-cooperative multi-agent game under uncertainty is formula ted as a two-stage stochastic variational inequality(SVI).Under standard assumptions,we provide sufficient conditions for the existence ...A convex two-stage non-cooperative multi-agent game under uncertainty is formula ted as a two-stage stochastic variational inequality(SVI).Under standard assumptions,we provide sufficient conditions for the existence of solutions of the two-stage SVI and propose a regularized sample average approximation method for solving it.We prove the convergence of the method as the regularization parameter tends to zero and the sample size tends to infinity.Moreover,our approach is applied to a two-stage stochastic production and supply planning problem with homogeneous commodity in an oligopolistic market.Numerical results based on historical data in crude oil market are presented to demonstrate the effectiveness of the two-stage SVI in describing the market share of oil producing agents.展开更多
This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model ar...This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.展开更多
基金the National Natural Science Foundation of China and Natural Science Foundation of Henan Province.
文摘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.
基金This work is supported by the Special Fund for Major State Basic Research Projects (G1999032805) the National Natural Science Foundation of China (10171106).
文摘This paper deals with fishing models with stage structure and harvest in an inshore-offshore area. By using the monotonic theory and concave operators to functional differential equations and the qualitative theory of differential equations, steady states of this dynamical systems representing fishery are derived, and their globally attracting behaviors are discussed. A brief biological meaning for the mathematical results is given.
文摘A convex two-stage non-cooperative multi-agent game under uncertainty is formula ted as a two-stage stochastic variational inequality(SVI).Under standard assumptions,we provide sufficient conditions for the existence of solutions of the two-stage SVI and propose a regularized sample average approximation method for solving it.We prove the convergence of the method as the regularization parameter tends to zero and the sample size tends to infinity.Moreover,our approach is applied to a two-stage stochastic production and supply planning problem with homogeneous commodity in an oligopolistic market.Numerical results based on historical data in crude oil market are presented to demonstrate the effectiveness of the two-stage SVI in describing the market share of oil producing agents.
文摘This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.
