Dynamics of a competitive population system with impulsive reduction of the invasive population
Texas State University, Department of Mathematics
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.
Competitive population system, Impulsive invasion, Extinction, Impulsive reduction, Permanence
Jiao, J., Cai, S., Liu, W., & Li, L. (2017). Dynamics of a competitive population system with impulsive reduction of the invasive population. <i>Electronic Journal of Differential Equations, 2017</i>(281), pp. 1-15.