Jianjun Jiao, Shaohong Cai, Wenjiang Liu, Limei Li
Abstract:
Biological invasion refers to the phenomenon that some organisms have been
accidentally or artificially introduced into the wild. The invasive
populations compete with the local population,and cause damage to the local
ecosystem. To protect the local ecosystem, the invasive populations should
be artificially reduced. Such processes are seldom studied in dynamical models.
In this work, we consider a competitive population system with
impulsive reduction of the invasive population.
All solutions of the investigated system are proved to be ultimately uniformly
bounded. Sufficient conditions are obtained to guarantee the linear stability
of the population x(t)-extinction periodic solution.
This signifies that the alien species invade successfully, and cause the
extinction of the native species. The permanency of the conditions is also
obtained, which shows that the alien species invade successfully, and they
coexist with the native species.
Numerical simulations are included to illustrate our results.
Through such computation, we find that there exists a threshold of
unsuccessful invasion, indicating that the native species cause the
extinction of the alien species. These results offer insights that impulsive
invasion plays an important role in the dynamics of ecosystem, and provide
some reliable tactical analysis for biological resources protection.
Submitted July 16, 2017. Published November 10, 2017.
Math Subject Classifications: 34D23, 92B05
Key Words: Competitive population system; impulsive invasion; extinction;
impulsive reduction; permanence.
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| Jianjun Jiao School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang 550004, China email: jiaojianjun05@126.com |
| Shaohong Cai School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang 550004, China email: caishaohong2014@126.com |
| Wenjiang Liu School of Mathematics and Statistics Guizhou University of Finance and Economics Guiyang 550004, China email: 1499353344@qq.com |
| Limei Li School of Continuous Education Guizhou University of Finance and Economics Guiyang 550004, China email: lilimei05@126.com |
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