to biological and chemical control strategy for pest control, a Holling II func- tional response predator-prey system concerning state-dependent impulsive control is investigated. We define the successor functions of ...to biological and chemical control strategy for pest control, a Holling II func- tional response predator-prey system concerning state-dependent impulsive control is investigated. We define the successor functions of semi-continuous dynamic system and give an existence theorem of order 1 periodic solution of such a system. By means of sequence convergence rules and quMitative analysis, we successfully get the conditions of existence and attractiveness of order 1 periodic solution. Our results show that our method used in this paper is more efficient and easier than the existing methods to prove the existence and attractiveness of order 1 periodic solution.展开更多
A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper.We introduce the basic reproduction number R0 first.Then the existence of endemic equilibrium(EE)can be determined by the sizes of...A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper.We introduce the basic reproduction number R0 first.Then the existence of endemic equilibrium(EE)can be determined by the sizes of R0 as well as the diffusion rates of susceptible and infected individuals.We also investigate the effect of diffusion rates on asymptotic profile of EE.Our results conclude that the infected population will die out if the diffusion rate of susceptible individuals is small and the total population N is below a certain level;while the two populations persist eventually if at least one of the diffusion rates of the susceptible and infected individuals is large.展开更多
This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov...This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.展开更多
Based on the facts of releasing natural enemies and spraying pesticides at different time points, we propose a generalized predator-prey model with impulsive interventions. The threshold values for the existence and s...Based on the facts of releasing natural enemies and spraying pesticides at different time points, we propose a generalized predator-prey model with impulsive interventions. The threshold values for the existence and stability of pest eradication periodic solution are provided under the assumptions of releasing natural enemies either more or less frequent than spray. In order to address how the different pulse time points, control tactics affect the pest control （i.e. the threshold value）, the Holling Type II Lotka-Volterra predator- prey system, as an example, with impulsive intervention at different time points axe investigated carefully. The numerical results show how the threshold values are affected by the factors including instantaneous killing rates of pesticides on pests and natural enemies, the release rate of natural enemies and release constant, timing of pesticide application and timing of release period. Furthermore, it is confirmed that the system has the coexistences of pests and natural enemies for a wide range of parameters and with quite different pest amplitudes.展开更多
文摘to biological and chemical control strategy for pest control, a Holling II func- tional response predator-prey system concerning state-dependent impulsive control is investigated. We define the successor functions of semi-continuous dynamic system and give an existence theorem of order 1 periodic solution of such a system. By means of sequence convergence rules and quMitative analysis, we successfully get the conditions of existence and attractiveness of order 1 periodic solution. Our results show that our method used in this paper is more efficient and easier than the existing methods to prove the existence and attractiveness of order 1 periodic solution.
基金the National Natural Science Foundation of China 61472471.
文摘A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper.We introduce the basic reproduction number R0 first.Then the existence of endemic equilibrium(EE)can be determined by the sizes of R0 as well as the diffusion rates of susceptible and infected individuals.We also investigate the effect of diffusion rates on asymptotic profile of EE.Our results conclude that the infected population will die out if the diffusion rate of susceptible individuals is small and the total population N is below a certain level;while the two populations persist eventually if at least one of the diffusion rates of the susceptible and infected individuals is large.
基金supported by the National Natural Science Foundation of China(Nos.11901398,11671149,11871225 and 11771102)Guangdong Basic and Applied Basic Research Foundation(No.2019A1515011350)the Fundamental Research Funds for the Central Universities(No.2018MS58).
文摘This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.
文摘Based on the facts of releasing natural enemies and spraying pesticides at different time points, we propose a generalized predator-prey model with impulsive interventions. The threshold values for the existence and stability of pest eradication periodic solution are provided under the assumptions of releasing natural enemies either more or less frequent than spray. In order to address how the different pulse time points, control tactics affect the pest control （i.e. the threshold value）, the Holling Type II Lotka-Volterra predator- prey system, as an example, with impulsive intervention at different time points axe investigated carefully. The numerical results show how the threshold values are affected by the factors including instantaneous killing rates of pesticides on pests and natural enemies, the release rate of natural enemies and release constant, timing of pesticide application and timing of release period. Furthermore, it is confirmed that the system has the coexistences of pests and natural enemies for a wide range of parameters and with quite different pest amplitudes.
