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ULTIMATE BEHAVIOR OF PREDATOR-PREY SYSTEM WITH CONSTANT HARVESTING OF THE PREY IMPULSIVELY
Dong, Lingzhen,Chen, Lansun,Sun, Lihua,Jia, Jianwen 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1
In this paper, we consider the Lotka- Volterra predator-prey system, in which constant quantity of the prey is harvested in regular pulses. The ultimate behavior of the solutions starting from different regions is mainly studied. Further, some examples are given to illustrate our results.
Hong Zhang,Lansun Chen 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.3
This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that R*< 1 the infection-free periodic solution is globally attractive, and that under the condition that R* > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic. This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that R*< 1 the infection-free periodic solution is globally attractive, and that under the condition that R* > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.
Ultimate behavior of predator-prey system with constant harvesting of the prey impulsively
Lingzhen Dong,Lansun Chen,Lihua Sun,Jianwen Jia 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1-2
In this paper, we consider the Lotka-Volterra predator-prey system, in which constant quantity of the prey is harvested in regular pulses. The ultimate behavior of the solutions starting from different regions is mainly studied. Further, some examples are given to illustrate our results.
Zhang, Hong,Chen, Lansun The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.3
This paper deals with a delayed SEIRS epidemic model with pulse vaccination and crowded incidence rate. Moreover, the case of vertical and horizontal transmission is considered. By using the discrete dynamical system determined by the stroboscopic map, the exact infection-free periodic solution of the SEIRS model is obtained. Further, by employing the comparison arguments, we prove that under the condition that $R_*$ < 1 the infection-free periodic solution is globally attractive, and that under the condition that $R^*$ > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.