The effect of state dependent delay and harvesting on a stage-structured predator–prey model

摘要

We propose and analyze a stage-structured predator–prey model in which the time from birth to maturity is directly related to the number of individuals present. Individuals mature more quickly when there are fewer of them around. The state dependent time delay is taken to be an increasing differentiable bounded function. In this research, we study the dynamics of our model analytically. We present results on positivity and boundedness of all populations. Criteria for the existence of all equilibria and uniqueness of a positive equilibrium are given. In order to observe the effect of state-dependent maturation delay, local stability analysis around all equilibria of the proposed model is discussed due to variation of maturation delay. Also, global stability of trivial and the boundary equilibria is investigated, using Liapunov functional and LaSalle invariant principle. To investigate the effect of state-dependent maturation delay and the harvesting effort of all species we carried out numerical simulations.