Journal of Applied Mathematics and Computing

, Volume 40, Issue 1, pp 445–457

Dynamics of the genic mutational rate on a population system with birth pulse and impulsive input toxins in polluted environment

Applied mathematics

DOI: 10.1007/s12190-012-0577-5

Cite this article as:
Jiao, J., Cai, S. & Chen, L. J. Appl. Math. Comput. (2012) 40: 445. doi:10.1007/s12190-012-0577-5


In this paper, we consider the genic mutation on an impulsive population system in polluted environment. All solutions of the investigated system are proved to be uniformly bounded. Using mathematical analysis methods, the conditions of the globally asymptotically stable population-extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is carried out illustrate our results. Our results provide reliable tactic basis for the practical biological resource management in polluted environment.


Population systemGenic mutationBirth pulsePolluted environmentExtinctionPermanence

Mathematics Subject Classification


Copyright information

© Korean Society for Computational and Applied Mathematics 2012

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, Guizhou Key Laboratory of Economic System SimulationGuizhou University of Finance and EconomicsGuiyangP.R. China
  2. 2.Institute of MathematicsAcademy of Mathematics and System SciencesBeijingP.R. China