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 differentia...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.展开更多
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 equilib...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.展开更多
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 e...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.展开更多
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 conti...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.展开更多
基金the National Natural Science Foundation of China(11871185)Zhejiang Provincial Natural Science Foundation of China(LY18A010010).
文摘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.
基金National Natural Science Foundation of China(No.11871185)Zhejiang Provincial Natural Science Foundation of China(LY18A010010).
文摘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.
基金supported by the National Natural Science Foundation of China(11871185)the Zhejiang Provincial Nat ural Science Foundation of China(LY18A010010).
文摘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.
基金This work was supported by the National Natural Science Foundation of China(11871185)Zhejiang Provincial Natural Science Foundation of China(LY18A010010).
文摘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.
