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Search Results: 1 - 10 of 78197 matches for " Lansun Chen "
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Global Dynamics Behaviors of Viral Infection Model for Pest Management
Chunjin Wei,Lansun Chen
Discrete Dynamics in Nature and Society , 2009, DOI: 10.1155/2009/693472
Abstract: According to biological strategy for pest control, a mathematical model with periodic releasing virus particles for insect viruses attacking pests is considered. By using Floquet's theorem, small-amplitude perturbation skills and comparison theorem, we prove that all solutions of the system are uniformly ultimately bounded and there exists a globally asymptotically stable pest-eradication periodic solution when the amount of virus particles released is larger than some critical value. When the amount of virus particles released is less than some critical value, the system is shown to be permanent, which implies that the trivial pest-eradication solution loses its stability. Further, the mathematical results are also confirmed by means of numerical simulation.
Harvesting Control for a Stage-Structured Predator-Prey Model with Ivlev's Functional Response and Impulsive Stocking on Prey
Kaiyuan Liu,Lansun Chen
Discrete Dynamics in Nature and Society , 2007, DOI: 10.1155/2007/86482
Abstract: We investigate a delayed stage-structured Ivlev's functional response predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for the biological resource management and enrich the theory of impulsive delay differential equations.
On a Periodic Time-Dependent Model of Population Dynamics with Stage Structure and Impulsive Effects
Kaiyuan Liu,Lansun Chen
Discrete Dynamics in Nature and Society , 2008, DOI: 10.1155/2008/389727
Abstract: We consider a periodic time-dependent predator-prey system with stage structure and impulsive harvesting, in which the prey has a life history that takes them through two stages, immature and mature. A set of sufficient and necessary conditions which guarantee the permanence of the system are obtained. Finally, we give a brief discussion of our results.
A Delayed Epidemic Model with Pulse Vaccination
Chunjin Wei,Lansun Chen
Discrete Dynamics in Nature and Society , 2008, DOI: 10.1155/2008/746951
Abstract: A delayed SEIRS epidemic model with pulse vaccination and nonlinear incidence rate is proposed. We analyze the dynamical behaviors of this model and point out that there exists an infection-free periodic solution which is globally attractive if 1<1, 2>1, and the disease is permanent. Our results indicate that a short period of pulse or a large pulse vaccination rate is the sufficient condition for the eradication of the disease. The main feature of this paper is to introduce time delay and impulse into SEIRS model and give pulse vaccination strategies.
Stage-Structured Impulsive Model for Pest Management
Ruiqing Shi,Lansun Chen
Discrete Dynamics in Nature and Society , 2007, DOI: 10.1155/2007/97608
Abstract: An SI epidemic model with stage structure is investigated. In the model, impulsive biological control is taken, that is, we release infected pests to the field at a fixed time periodically. We get a sufficient condition for the global asymptotical stability of the pest-eradication periodic solution (0,0,I?(t)), and a condition for the permanence of the system. At last, a brief discussion shows that our results will be helpful for pest management.
Periodic Solution of Prey-Predator Model with Beddington-DeAngelis Functional Response and Impulsive State Feedback Control
Chunjin Wei,Lansun Chen
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/607105
Abstract: A prey-predator model with Beddington-DeAngelis functional response and impulsive state feedback control is investigated. We obtain the sufficient conditions of the global asymptotical stability of the system without impulsive effects. By using the geometry theory of semicontinuous dynamic system and the method of successor function, we obtain the system with impulsive effects that has an order one periodic solution, and sufficient conditions for existence and stability of order one periodic solution are also obtained. Finally, numerical simulations are performed to illustrate our main results.
Extinction and Permanence of a General Predator-Prey System with Impulsive Perturbations
Xianning Liu,Lansun Chen
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/521729
Abstract: A general predator-prey system is studied in a scheme where there is periodic impulsive perturbations. This scheme has the potential to protect the predator from extinction but under some conditions may also serve to lead to extinction of the prey. Conditions for extinction and permanence are obtained via the comparison methods involving monotone theory of impulsive systems and multiple Liapunov functions, which establish explicit bounds on solutions. The existence of a positive periodic solution is also studied by the bifurcation theory. Application is given to a Lotka-Volterra predator-prey system with periodic impulsive immigration of the predator. It is shown that the results are quite different from the corresponding system without impulsive immigration, where extinction of the prey can never be achieved. The prey will be extinct or permanent independent of whether the system without impulsive effect immigration is permanent or not. The model and its results suggest an approach of pest control which proves more effective than the classical one.
Dynamical Analysis of a Delayed Predator-Prey System with Birth Pulse and Impulsive Harvesting at Different Moments
Jiao Jianjun,Chen Lansun
Advances in Difference Equations , 2010,
Abstract: We consider a delayed Holling type II predator-prey system with birth pulse and impulsive harvesting on predator population at different moments. Firstly, we prove that all solutions of the investigated system are uniformly ultimately bounded. Secondly, the conditions of the globally attractive prey-extinction boundary periodic solution of the investigated system are obtained. Finally, the permanence of the investigated system is also obtained. Our results provide reliable tactic basis for the practical biological economics management.
Dynamical Analysis of a Delayed Predator-Prey System with Birth Pulse and Impulsive Harvesting at Different Moments
Jianjun Jiao,Lansun Chen
Advances in Difference Equations , 2010, DOI: 10.1155/2010/954684
Abstract:
Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy
Min Zhao,Yanzhen Wang,Lansun Chen
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/969425
Abstract: The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.
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