Analysis of Ecological Model With Holling Type Iv Functional Response

Abstract

In this paper a three-species of predator-prey food chain model with Holling type IV functional response is proposed. The boundedness of the solution of the model is discussed.Stability analysis of the system is carried out. The dynamics of the predator-prey food chain model with simplified Holling type IV functional response is investigated theoretically as well as numerically.

Controlling Chaotic Dynamics of a Continuous Ecological Model

“…There are at most four non-negative equilibrium points E 0 , E 1 , E 2 and the interior equilibrium point E 3 which is left aside, see [15,23]. Now the existence and stability conditions of the above equilibrium points are given below:…”

“…Ayala [10] proved experimentally that two species of Drosophila could coexist upon a single limit resource. Ayala's experiment leads to a large body of work, which continuous to this day, see [1,2,6,8,[15][16][17][19][20][21][22][23][24][25]. Upadhyay [20] studied Rosenzweig-McArthur [18] model to investigate the existence of complex dynamical behavior in a food chain model involving Holling type IV functional response of the form wx d+x+x 2 /i and the effects of the intraspecific competition in the first level of the model is also studied.…”

Qualitative Analysis of Food-Web Model through Diffusion-Driven Instability

“…The most realistic and natural three-species food chain is one in which the middle predator is a specialist (species that can survive in the presence of preferred food). Another is that the top predator is a generalist (a species that can survive without its preferred meal), according to [5][6][7][8]. We looked at a three-species food chain in our post, with prey, middle, and apex predators.…”

Chaos in a Hybrid Food Chain Model

“…The works of Lotka [1] and Volterra [2] are the most major works in mathematical models and dynamical systems. Researchers in ecology and engineering reported the essence of chaos [3][4][5][6][7][8][9][10][11][12]. In the analysis of the mechanical model, the geometrical non-linearity, represented by the pendulum, may lead to chaotic dynamics [4,13].…”