| Volume 7, Number 2, 2017, Pages 439-454 DOI：10.11948/2017028 |
| On period-$k$ solution for a population system with state-dependent impulsive effect |
| Xiaowei Tang,Xilin Fu |
| Keywords:Period-$k$ solution, local stability, mapping structure, trajectory direction. |
| Abstract: |
| The period-$k$ solutions of population differential system with state-dependent impulsive effect are investigated by the theory of discontinuous dynamical system. Through $G$-function theory, the necessary and sufficient conditions are obtained for trajectory direction of a population differential system, and the results are better than the previous work. Also, the local stability of period-$k$ solutions is studied by the mapping structure and the theory of eigenvalue analysis. Furthermore, the existence of period-1 solution is investigated for a special impulsive population differential system, and the analytical condition is established. Finally, the trajectory of period-1 solution and the relationship between different parameters and the module of eigenvalues are illustrated. |
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