A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of pr...A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.展开更多
By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional respon...By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional response in a periodic environment.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 nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence...The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.展开更多
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic beh...The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.展开更多
By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficien...By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.展开更多
The CPB （Colorado potato beetle）, Leptinotarsa decemlineata （Say）, is the major insect pest of potato crops in North America, Europe and Asia. Large amounts of chemical insecticides are used to control this insect...The CPB （Colorado potato beetle）, Leptinotarsa decemlineata （Say）, is the major insect pest of potato crops in North America, Europe and Asia. Large amounts of chemical insecticides are used to control this insect pest. Also, the CPB has developed over the years a resistance to most of the registered chemical insecticides, including those that were effective at one time. One of the most promising alternatives to chemical insecticides consists of taking advantage of natural enemies. The use of the stinkbug predator Perillus bioculatus to control the CPB has been successful at small scale. However, this natural enemy is not abundant in the nature and its hand release at large scale is not realistic. To remedy to this problem, predators must be massively released in potato fields using a mechanical distributor. Such a machine has been successfully designed and built at the Department of Soils and Agri-Food Engineering of University Lavak In this distributor, masses of predators are placed in small containers and mixed with a carrier material. In the field, the containers are mechanically opened at different locations, based on a source-point mass release option. These locations are determined in advance following a field monitoring of the populations of CPBs. Field trials proved that the mechanical distributor is reliable and ease of use. Its efficiency in releasing insect predators is high and comparable to that obtained in previous laboratory tests.展开更多
In this paper, a nonautonomous predator-prey dispersion model is studied, where all parameters are time-dependent. The system, which is consisted of n-patches, the prey specics can disperse among n-patches, but the pr...In this paper, a nonautonomous predator-prey dispersion model is studied, where all parameters are time-dependent. The system, which is consisted of n-patches, the prey specics can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved the system is uniformly persistent under any dispersion rates effect. Furthermore, sufficient conditions are established for global stability of the system.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（10771179） Supported by the Natural Science Foundation of the Education Department Henan Province（2007110028）
文摘A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.
文摘By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions of a delayed predator prey system with nonmonotonic functional response in a periodic environment.
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.
基金Important Study Project of the NationalNatural Science F oundation of China( No.90 2 110 0 4),and"Hun-dred Talents Project"of Chinese Academy of Sciences
文摘The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
文摘The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
基金Supported by the Science Foundation of Hangzhou Dianzi University(KYF091504021)Supported by the Science Foundation of China Jiliang University(XZ0442)
文摘By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.
文摘The CPB （Colorado potato beetle）, Leptinotarsa decemlineata （Say）, is the major insect pest of potato crops in North America, Europe and Asia. Large amounts of chemical insecticides are used to control this insect pest. Also, the CPB has developed over the years a resistance to most of the registered chemical insecticides, including those that were effective at one time. One of the most promising alternatives to chemical insecticides consists of taking advantage of natural enemies. The use of the stinkbug predator Perillus bioculatus to control the CPB has been successful at small scale. However, this natural enemy is not abundant in the nature and its hand release at large scale is not realistic. To remedy to this problem, predators must be massively released in potato fields using a mechanical distributor. Such a machine has been successfully designed and built at the Department of Soils and Agri-Food Engineering of University Lavak In this distributor, masses of predators are placed in small containers and mixed with a carrier material. In the field, the containers are mechanically opened at different locations, based on a source-point mass release option. These locations are determined in advance following a field monitoring of the populations of CPBs. Field trials proved that the mechanical distributor is reliable and ease of use. Its efficiency in releasing insect predators is high and comparable to that obtained in previous laboratory tests.
基金Supported by the Natural Science Foundatioll of Henan province (994051600)
文摘In this paper, a nonautonomous predator-prey dispersion model is studied, where all parameters are time-dependent. The system, which is consisted of n-patches, the prey specics can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. It is proved the system is uniformly persistent under any dispersion rates effect. Furthermore, sufficient conditions are established for global stability of the system.
