Abstract
This work considers a stage-structured predator–prey harvesting system with anti-predator behavior. It discusses the impact of the selective harvesting of a species above a specific age or size by incorporating time delays in the harvesting terms. Analytical and numerical simulation of the proposed system suggest that the coexistence steady state is stable at low and moderate values of the delay parameter associated with the maturation of the predator. However, there is an interval of maturation delay where the system exhibits oscillatory behavior. A very long maturation time can cause the extinction of the predator species. The effect of anti-predator behavior on the proposed system is analyzed. Moreover, the time delays associated with harvesting of prey and adult predator, while crossing some threshold values, drive the system toward instability. There also have some interesting results based on the harvesting rate.
