Affiliation:
1. Taiyuan University of Technology
2. Dalian University of Technology
Abstract
With some theory about continuous and impulsive dynamical system, an impulsive model based on a special predator-prey system is considered. We assume that the impulsive effects occur when the density of the prey reaches a given value. For such a state-dependent impulsive system, the existence, uniqueness and orbital asymptotic stability of an order-1 periodic solution are discussed. Further, the existence of an order-2 periodic solution is also obtained, and persistence of the system is investigated.
Publisher
Trans Tech Publications, Ltd.
Reference12 articles.
1. D. Bainov, P. Simeonov, Impulsive differential equations: Periodic solution and Applications, Pitman Monographs and Surveys in Pure and Applied Mathematics, (1993)66.
2. K. Chen, Uniqueness of a limit cycle for a predator-prey system, SIAM J. Math. Anal, 1981(12): 541-548.
3. Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., Knuth, D. E., On the Lambert W function, Advances in Computational Mathematics, 1996(5): 329-359.
4. J. M. Cushing, Periodic time-dependent predator-prey system, SIAM J. Appl. Math, 1977(32): 82-95.
5. Eric Funasaki, Mark Kor, Invasion and chaos in a periodically pulsed mass-action chemostat, Theoretical population Biology, 1993(44): 203-224.