Species extinction and permanence in a prey–predator model with two-type functional responses and impulsive biological control

By introducing impulsive biological control strategy, the dynamic behaviors of the two-prey one-predator model with defensive ability and Holling type-II functional response are investigated. By using Floquet’s Theorem and the small amplitude perturbation method, we prove that there exists an asympt...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2008-04, Vol.52 (1-2), p.71-81
Main Authors: Pei, Yongzhen, Zeng, Guangzhao, Chen, Lansun
Format: Article
Language:English
Subjects:
Automotive Engineering
Biological control
Classical Mechanics
Computer simulation
Control
Dynamical Systems
Engineering
Liapunov functions
Mechanical Engineering
Original Paper
Perturbation methods
Predator-prey simulation
Vibration
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:By introducing impulsive biological control strategy, the dynamic behaviors of the two-prey one-predator model with defensive ability and Holling type-II functional response are investigated. By using Floquet’s Theorem and the small amplitude perturbation method, we prove that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical minimum value, and permanence conditions (that is, the impulsive period is greater than some critical maximum value) are established via the method of comparison involving multiple Liapunov functions. It is shown that our impulsive control strategy is more effective than the classical one. Furthermore, the effect of impulsive perturbations on the unforced continuous system is studied. From simulations, we find that the system has more complex dynamic behaviors and is dominated by periodic, quasi-periodic, and chaotic solutions.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-007-9258-6