A Stage-Structure Rosenzweig-MacArthur Model with Effect of Prey Refuge

Abstract

We proposed and analyzed a stage-structure Rosenzweig-MacArthur model incorporating a prey refuge. It is assumed that the prey is a stage-structure population consisting of two compartments known as immature prey and mature prey. The model incorporates the functional response Holling type-II. In this work, we investigate all the biologically feasible equilibrium points, and it is shown that the system has three equilibrium points. Sufficient conditions for the local stability of the non-negative equilibrium point of the model are also derived. All points are conditionally locally asymptotically stable. By constructing Jacobian matrix and determined eigenvalues, we analyzed the local stability of the trivial equilibrium and non-predator equilibrium points. Specifically for coexistence equilibrium point, Routh-Hurwitz criterion used to analyze local stability. In addtion, we investigated the effect of immature prey refuge. Our mathematical analysis exhibits that immature prey refuge have played a crucial role in the behavioral system. When the effect of immature prey refuge (constant m) increases, it is can stabilize non-predator equilibrium point, where all the species can not exists together. And conversely, if contant m decreases, it is can stabilize coexistence equilibrium point then all the species can exists together. The work is completed with a numerical simulation to confirmed analitical results

Fear effect in discrete prey-predator model incorporating square root functional response

“…The prey-predator model, still now an exciting topic in mathematical biology. Most of this ecological problem which studies the interaction between a prey and its predator is modeled by deterministic approach using firstorder differential equation [1][2][3][4][5], fractional-order differential equation [6][7][8], or with discrete-time equation [9][10][11][12][13]. Particularly, discrete models are an essential tool for mathematical biology problems.…”

Dynamics of a stage–structure Rosenzweig–MacArthur model with linear harvesting in prey and cannibalism in predator

“…We assume that the predator does not attack and eat the mature prey. A conversion rate of the consumed prey into the predator birth is ϕ, and next, δ 2 denotes the per capita death rate of the predator [6][7][8]. Now, we consider the harvesting and cannibalism processes to modify the stage-structure predator-prey model in [6].…”

“…Note that the local stability of the system (1) was investigated by Beay et al [6]. Furthermore, dynamics of the system (1) with prey refuge was studied by Beay and Saija [7]. Next, in [8] Beay et al consider intraspecific competition in the system.…”

Dynamics in two competing predators-one prey system with two types of Holling and fear effect

“…Since Lotka (1925) and Volterra (1931) proposed the predator-prey model known as the Lotka-Volterra model, the mathematical modeling of the ecological model has progressed rapidly. This model is the forerunner of other predator-prey model, such as Leslie-Gower model [1][2][3][4][5] and Rosenzweig-MacArthur model [6][7][8][9]. The dynamic behavior of predator-prey model can be influenced by many factors, such as mortality rates, competition between species, fear of prey, infectious disease, and environment conditions.…”