Dynamics in a delayed differential-algebraic model with stage structure and diffusion

A delayed differential-algebraic bio-economic model is proposed, which is utilized to investigate interaction and coexistence mechanism of biological population in the harvested ecosystem due to the variation of population spatial diffusion and gestation delay. Local stability of the proposed model with gestation delay and diffusion is studied, which reveals that the interior equilibrium loses its stability at some critical values of gestation delay and corresponding cycle occurs. It is also shown that population spatial diffusion and harvesting have a stabilizing effect on population dynamics. Finally, numerical simulations are carried out to show consistency with theoretical analysis obtained in this paper.