为了证明一类在周期环境中带时滞的三种群食物链系统的正周期解的存在性和全局吸引性,利用 Gains and Mawhin’s的重合度延拓定理,并通过构造一个恰当的李雅普诺夫函数找出了这个正周期解的全局吸引性的充分条件．在这个模型中,考虑三...为了证明一类在周期环境中带时滞的三种群食物链系统的正周期解的存在性和全局吸引性,利用 Gains and Mawhin’s的重合度延拓定理,并通过构造一个恰当的李雅普诺夫函数找出了这个正周期解的全局吸引性的充分条件．在这个模型中,考虑三个种群——y1,y2,y3,其中y1是y2的食饵,y2是y3的食饵;还考虑了作为一类种群,其独立生存时的增长率(主要是y1)和独立生存时的死亡率(主要是y2和y3)以及种群之间相互的掠夺和供养等能力．由于这类模型既考虑了种群竞争,又考虑了种群依存,所以在估计先验界时需要对这三个种群分别进行,而且对解的上下界的估计要更精确,否则得不到合理的先验界．展开更多
In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilib...In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed, and then uniformly persistent sufficient conditions of populations were found.展开更多
two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, ...two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, by the comparison theorem of impulsive differential equation, the sufficient conditions are derived for the permanence and the existence of periodic solution of the system.展开更多
The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the ...The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.展开更多
A predator-prey discrete-time model with non-monotone functional response and den- sity dependence is investigated in this paper. By using the comparison theorem of the difference equation, some sufficient conditions ...A predator-prey discrete-time model with non-monotone functional response and den- sity dependence is investigated in this paper. By using the comparison theorem of the difference equation, some sufficient conditions are obtained for the permanence of the system with variable coefficients. At the same time, a set of sufficient conditions about permanent of the system with almost periodic coefficients is also set up, which utilizes almost periodic characteristics of the system. Furthermore, the criteria which guarantee the existence of a globally attractive positive almost periodic solution of the system is established. An example is given to illustrate the feasibility of the obtained results.展开更多
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
基金Supported by the National Natural Science Foundation of Educational Department of China(10471117,10526015)Scientif-ic Research Foundation of Guangxi Province(2006243).
文摘为了证明一类在周期环境中带时滞的三种群食物链系统的正周期解的存在性和全局吸引性,利用 Gains and Mawhin’s的重合度延拓定理,并通过构造一个恰当的李雅普诺夫函数找出了这个正周期解的全局吸引性的充分条件．在这个模型中,考虑三个种群——y1,y2,y3,其中y1是y2的食饵,y2是y3的食饵;还考虑了作为一类种群,其独立生存时的增长率(主要是y1)和独立生存时的死亡率(主要是y2和y3)以及种群之间相互的掠夺和供养等能力．由于这类模型既考虑了种群竞争,又考虑了种群依存,所以在估计先验界时需要对这三个种群分别进行,而且对解的上下界的估计要更精确,否则得不到合理的先验界．
文摘In this paper, we considered the predator-prey system with stage-structure for prey, where the predators predate immature preys only. The positivity and boundedness of the solutions and asymptotic stability of equilibrium were firstly discussed, and then uniformly persistent sufficient conditions of populations were found.
基金Supported by the Education Department Natural Science Foundation of Henan Province （2008A180041）
文摘two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, by the comparison theorem of impulsive differential equation, the sufficient conditions are derived for the permanence and the existence of periodic solution of the system.
文摘The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.
文摘A predator-prey discrete-time model with non-monotone functional response and den- sity dependence is investigated in this paper. By using the comparison theorem of the difference equation, some sufficient conditions are obtained for the permanence of the system with variable coefficients. At the same time, a set of sufficient conditions about permanent of the system with almost periodic coefficients is also set up, which utilizes almost periodic characteristics of the system. Furthermore, the criteria which guarantee the existence of a globally attractive positive almost periodic solution of the system is established. An example is given to illustrate the feasibility of the obtained results.
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.
