Dynamic Analysis Of A Tri-trophic Food Chain Model With Fear Factors

The dynamic relationships in organisms have important biological significance and have always been an important research topic in biomathematics.This paper introduces the fear from the top predator on the predator and the fear from the predator on the prey,based on a tri-trophic food chain model with Holling-IV and B-D functional responses,getting a new model.In theory,this paper simplifies the new model and explores the boundedness,extinction,persistence,existence,local stability.Poincare s cut curve method and Lyapunov functions are used to prove the global stability of equilibrium points.In numerical analysis,if there is no fear factor,the original system can show stable focus,period oscillation and chaos.In this paper,we will explore the impact of fear factors on the original system in different situations.Our numerical simulations show the fear factors can affect the population dynamics,and a way to get specific population relationships is investigated.Both fears can change the periodic oscillations to stable focus,reduce the amplitude,and change the stability of equilibrium point.Under certain circumstances,the fear from predator is more powerful to change this situation and less time-consuming.Furthermore,when the fear from predator increases,the system can transform the chaos into stable focus,and then turn the stable focus into periodic oscillations again and meanwhile a semi-stable limit cycle appears.But the fear on the middle predator has little effect on the structure of chaos.