Abstract
In this work, a prey-predator model with both state-dependent impulsive harvesting and constant rate harvesting is investigated, where the replenishment rate of prey and the harvesting rate are linearly related with the selected threshold. By first using the successor function method and differential equation geometry theory, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed. And then numerical simulations with an example are given to illustrate the feasibility of the theorem-related results. Moreover, in order to increase the total profit, the optimization strategy is presented and the optimal threshold is obtained.
Highlights
Fishery is the natural source and basis of fishery production, and it is one of the important food sources for human beings
Jiao et al [18] considered a periodic impulsive harvesting prey-predator system with prey hibernation, and they obtained the conditions of the global asymptotic stability criterion for the predator-extinction boundary and the permanent conditions
4.2 Determination of optimal threshold h The practical significance of studying the order-1 periodic solution is that it provides the possibility to determine the replenishment rate of prey fish and the harvesting rate of predator fish, which makes the impulsive control to be not a real-time monitoring of fisheries, but rather a periodic one
Summary
Fishery is the natural source and basis of fishery production, and it is one of the important food sources for human beings. After further research on renewable resources, Huang et al [40, 41] combined constant rate harvesting with state-dependent impulse harvesting, and introduced a real-time monitoring system, further improved the harvesting approach. They proved the existence, uniqueness and stability of periodic solution. When implementing impulse strategy, they only considered the harvest of the predator, while ignoring that the prey was harvested at the same time, and the control parameters were not linearly related to the threshold.
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