Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1100.92071
Lu, Zhonghua; Chi, Xuebin; Chen, Lansun
Impulsive control strategies in biological control of pesticide. (English)
[J] Theor. Popul. Biol. 64, No. 1, 39-47 (2003). ISSN 0040-5809

Summary: By presenting and analyzing a pest-predator model under insecticides used impulsively, two impulsive strategies in biological control are put forward. The first strategy: the pulse period is fixed, but the proportional constant $E_1$ changes, which represents the fraction of pests killed by applying insecticides. For this scheme, two thresholds, $E_1^{**}$ and $E_1^*$ for $E_1$ are obtained. If $E_1\ge E_1^*$, both the pest and predator (natural enemies) populations go to extinction. If $E_1^{**}<E_1<E_1^*$, the pest population converges to the semi-trivial periodic solution while the predator population tends to zero. If $E_1$ is less than $E_1^{**}$ but even if close to $E_1^{**}$, there exists a unique positive periodic solution via bifurcation, which implies both the pest and the predator populations oscillate with a positive amplitude. In this case, the pest population is killed to the maximum extent while the natural enemies are preserved to avoid extinction. The second strategy: the proportional constant $E_1$ is fixed $(E_1<E_1^*$ firstly), but the pulse period changes. For this scheme, one threshold $\tau_0$ for the pulse period $\tau$ is obtained. We can reach the same target as above by controlling the period impulsive effect $\tau<\tau_0$, even if close to $\tau_0$. Our theoretical results are confirmed by numerical simulations.

MSC 2000:: *92D40 Ecology
93C15 Control systems governed by ODE
93C95 Appl. of control theory
34A37 Differential equations with impulses

Keywords: biological control; periodic predator-free solution; threshold; asymptotically stable

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]