Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 1162.34007
Nie, Linfei; Peng, Jigen; Teng, Zhidong; Hu, Lin
Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects. (English)
[J] J. Comput. Appl. Math. 224, No. 2, 544-555 (2009). ISSN 0377-0427

An impulsive system of Lotka-Volterra-predator-prey type, according to biological and chemical control strategy for pest is constructed $$\aligned & \left.\aligned & \frac{dx}{dt}=x(t)[b_1-a_{11} x(t)-a_{12} y(t)]\\ & \frac{dy}{dt}=y(t)[-b_2+a_{21}x(t)]\endaligned\right\}\ x\ne h_1h_2,\\ & \left.\aligned & \Delta x(t)=0\\ & \Delta y(t)=y(t^+)-y(t)=\alpha\endaligned\right\}\quad x=h_1\\ & \left.\aligned & \Delta x(t)=x(t^+)-x(t)=-px(t)\\ & \Delta y(t)=y(t^+)-y(t)=-qy(t)\endaligned\right\}\quad x=h_2\endaligned\tag1$$ Sufficient conditions for the existence of -- stable semi-trivial solution of (1) -- order-1 periodic solution of (1) -- positive locally orbitally stable solution of (1) -- positive order-1 periodic solution are founded.
[Stepan Kostadinov (Plovdiv)]

MSC 2000:: *34A37 Differential equations with impulses
34C25 Periodic solutions of ODE
92D25 Population dynamics

Keywords: impulsive differential equations; Runge-Kutta method for stochastic differential equations; Lotka-Volterra predator-prey system

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]