Oscillations, fluctuation intensity and optimal harvesting of a bio-economic model in a complex habitat

We investigate the effects of habitat complexity and multi-time delays on dynamics of a bio-economic predator–prey model. The differential–algebraic system theory is applied to transform the bio-economic model into a normal form, so that the local stability and existence of periodic solutions can be examined by varying the delays and the habitat complexity parameter. The direction of Hopf bifurcation and the stability of bifurcated periodic solutions are investigated. We also discuss the effect of fluctuating environment on dynamical behavior of a corresponding stochastic delayed-differential–algebraic system and derive expressions for intensities of population fluctuations. The model is also used to study the optimal harvesting strategy in order to maximize economic profit while sustaining the ecosystem. Numerical simulations are designed to illustrate the effectiveness of theoretical analysis.