Abstract
In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results.
Highlights
In recent years, for modelling the dynamics of some biological populations, several delay differential systems of logistic type have been proposed and studied by many authors; see [2, 4, 5, 7, 9, 13, 19, 29, 31]
Our result shows that the persistence of system (4) can be guaranteed if the impulsive functions Ik vary in a certain degree and the lower bound of the impulsive interval is greater than a certain constant
Our result shows that the persistence of system (4) with time-varying delays and impulsive perturbations can be guaranteed if the impulsive functions Ik vary in a certain degree and the lower bound of the impulsive interval is greater than a certain constant
Summary
For modelling the dynamics of some biological populations, several delay differential systems of logistic type have been proposed and studied by many authors; see [2, 4, 5, 7, 9, 13, 19, 29, 31]. For fishery management and many other harvesting situations, it is unreasonable to assume that the harvesting rate (i.e., bk) is periodic (it may be dependent on the population density), and sometimes it is difficult to guarantee the harvesting time is periodic due to human factor and weather variations Another example, considering the metapopulation models, a species may migrate from one place to another place according to the seasons.
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