Qualitative Analysis of Prey-Predator Model With Nonlinear-Impulsive Effects

WANG Gang; TANG San-yi

doi:10.3879/j.issn.1000-0887.2013.05.008

Volume 34 Issue 5

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WANG Gang, TANG San-yi. Qualitative Analysis of Prey-Predator Model With Nonlinear-Impulsive Effects[J]. Applied Mathematics and Mechanics, 2013, 34(5): 496-505. doi: 10.3879/j.issn.1000-0887.2013.05.008

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Qualitative Analysis of Prey-Predator Model With Nonlinear-Impulsive Effects

doi: 10.3879/j.issn.1000-0887.2013.05.008

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062,P.R.China

Received Date: 2013-04-03
Rev Recd Date: 2013-05-03
Publish Date: 2013-05-15

Abstract

Abstract

Due to the limited resources as well as the development of pests’ resistance to pesticides, the instant killing rate of pesticide applications with respect to the pest could depend on the density of pest populations. Thus, the instant killing rate is a function of economic threshold ET once the density of pest population reaches the ET and integrated control tactics are implemented. In order to depict the saturation effects, a prey-predator model with nonlinear state-dependent impulsive effects was proposed. Using the Lambert W function and the analytical techniques of the impulsive semi-dynamical system, the sufficient conditions which guaranteed the existence, local and global stability of order 1 positive periodic solution of the proposed model were obtained. Further, the effects of nonlinear impulse on the existence of order 1 periodic solution was discussed.
- nonlinear pulse,
- preypredator model,
- order 1 periodic solution,
- existence,
- stability

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References(10)

References

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