摘要
A differential-algebraic prey--predator model with time delay and Allee effect on the growth of the prey population is investigated. Using differential-algebraic system theory, we transform the prey predator model into its normal form and study its dynamics in terms of local analysis and Hopf bifurcation. By analyzing the associated characteristic equation, it is observed that the model undergoes a Hopf bifurcation at some critical value of time delay. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, and an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.
基金
This work was supported by National Science Foundation of China 61273008 and 61203001, Doctor Startup Fund of Liaoning Province （20131026）, Fundamental Research Funds for the Central University （N140504005） and China Scholarship Council. The authors gratefully thank referees for their valuable suggestions.
