Dynamics of the Oscillative Solution for a Non-Linear Ecosystem with Impulsive Perturbation


Article Preview

In the present paper, we investigate an impulsive predator-prey model of integrated pest management(IPM) strategy. Other than the general Holling's functional response, an S-shaped mixed functional response is considered, simultaneously, we model this system assuming that the releasing of nature enemies and spraying of pesticides are impulsive at different fixed moment, which is more realistic comparing with at the same time. With the help of Floquet's theorem, small amplitude perturbation skills and comparison theorem involving multiple Liapunov functions, we show that under some sufficient conditions, the system exists an oscillative pest eradication periodic solution, which is local stable and globally attractive. Otherwise, the system is permanent. This result(threshold) provides us a very useful information for the control of ecosystem.



Edited by:

Chunliang Zhang and Paul P. Lin




Y. S. Tan and H. Zhang, "Dynamics of the Oscillative Solution for a Non-Linear Ecosystem with Impulsive Perturbation", Applied Mechanics and Materials, Vols. 226-228, pp. 474-478, 2012

Online since:

November 2012




[1] R. Van den osc: The Pesticide Conspiracy. Doubleday(Co, Garden City, NY 1978).

[2] S.Y. Tang, Y.N. Xiao, L.S. Chen and R.A. Cheke: Bulletin of Mathematical Biology, Vol. 67(2005), p.115.

[3] D.D. Bainov and P.S. Simeonov: Impulsive differential equations: periodic solutions and applications( London, Longman, 1993).

[4] V. Laksmikantham, D.D. Bainov and P.S. Simeonov: Theory of Impulsive Differential Equations(World Scientific, Singapore, 1993).

[5] A. Donofrio: Math. Biosci., Vol. 172(2002), p.52.

[6] B. Liu and L.S. Chen: Math. Med. Biol., Vol. 21(2004), p.129.