Qualitative Analysis On A Class Of Predator-prey Systems With Holling-IV Type Functional Response Function

Population ecology is one of the important research areas in biomathematics. The constraintsbetween different species have become an important issue in biological invasion. Constraints betweendifferent populations can be represented by functions, called functional response functions.Depending on the species, functional response functions can be divided into many categories, such asHolling type, Beddington type, etc. This paper mainly studies the prey-predator system withfunctional response function of Holling-IV type, which has been widely applied in populationecology.Firstly, this paper introduces current research progress of the prey-predator system withfunctional response function of Holling-IV type. Secondly, for this system, the paper discusses theexistence and stability of the equilibrium points, boundedness of solutions with positive initialconditions, nonexistence and existence conditions of limit cycles. Thirdly, with the theory oftime-delay differential equations, the paper studies the system with time-delay in the aspects ofstability and Hopf bifurcation of the equilibrium points, and obtains some sufficient conditions for thestability and bifurcation of the time-delay system. Finally, with the theory of impulsive differentialequations, the paper studies the system with impulse, and obtains some sufficient conditions on thestability and persistence of the impulsive system.