J4 ›› 2012, Vol. 47 ›› Issue (9): 98-104.

• Articles • Previous Articles     Next Articles

The periodic solution for a class of competition system with proportional and constant impulse harvesting

LU La-la, DOU Jia-wei   

  1. College of Mathematics and Information Science, Shaanxi Normal University,  Xi’an 710062, Shaanxi, China
  • Received:2011-05-03 Online:2012-09-20 Published:2012-09-24

Abstract:

The existence of the positive periodic solution was studied for a class of periodic logistic equation with impulsive harvesting, which includes both cases of the proportional and constant harvesting. Then, based on the results obtained for logistic equation, a monotone-iterative scheme was established to obtain the existence of the positive periodic solutions for Lotka-Volterra competition system. This method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic solution. An example was given and some computer simulations were carried out to demonstrate the main results.

Key words: Lotka-Volterra competition system; proportional and constant impulse harvesting; monotone-iterative method; periodic solution

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