DeAngelis Functional Response Research Articles

Dynamical Behavior of Two Predators-One Prey Ecological System with Refuge and Beddington –De Angelis Functional Response

Dynamical Behavior of Two Predators-One Prey Ecological System with Refuge and Beddington –De Angelis Functional Response

Dynamics of Rodent Population With Two Predators

Modeling rodent populations has been always a challenge for population ecologists. These populations have oscillations that are dynamically complex. In this paper, we consider the population dynamics of rodents under the effect of the “specialist” and “generalist” predators with Beddington–DeAngelis and sigmoidal functional responses. We discover that the ODE system has one axial state and two boundary states. If the rate of predation by the generalist predator is more than the critical value \((c_2>c_2^*)\), then the system has a unique internal equilibrium which is stable if the predator’s intrinsic growth rate of population is more than the critical value \(s^*\). We show that the predation rates of the both predators (\(c_1, c_2\)) play an important role on rodent population dynamic. Then, we have considered a delay differential equation (DDE) model to account for the time delays in the transient dynamics. By treating time delays as the bifurcation parameter, we show that a Hopf bifurcation about the equilibria could happen for critical time delays. Finally, we gave an biological interpretation of our analytical results.

Bifurcation and spatiotemporal patterns in a Bazykin predator-prey model with self and cross diffusion and Beddington-DeAngelis response

In this article, the clasical Bazykin model is modifed with Bedding–ton–DeAngelis functional response, subject to self and cross-diffusion, in order to study the spatial dynamics of the model.We perform a detailed stability and Hopf bifurcation analysis of the spatial model system and determine the direction of Hopf bifurcation and stability of the bifurcating periodic solutions. We present some numerical simulations of time evolution of patterns to show the important role played by self and cross-diffusion as well as other parameters leading to complex patterns in the plane.

Global stability of a predator-prey model with Beddington–DeAngelis and Tanner functional response

Global stability of a predator-prey model with Beddington–DeAngelis and Tanner functional response

Effects of Nonlinear Growth and Death Rates for the Predator in Predator-Prey Type Models

Following a recent paper by Terry [1] and a recent work of the two authors [2], in the present work we study the effects of nonlinear (w.r.t. the functional response) growth and death ratesfor the predator by comparing models incorporating such rates with the classical models with a linear growth rateand a constant death rate. We study a three-dimensional ODE system modelling the interactions between a predator population andtwo independent preys---existence and stability of equilibria, persistence conditions, etc. as well asuse numerical simulations in order to make comparison with the classical models, see e.g. [3]. Refernces: [1] A.J. Terry, A predator-prey model with generic birth and death rates forthe predator, Mathematical Biosciences 248 (2014) 57-66. [2] T. Ivanov, N. Dimitrova, A predator-prey model with generic birth and death rates for the predator and Beddington--DeAngelis functional response. Submitted. [3] R.K. Naji, A.T. Balasim, On the dynamical behavior of three species food web model,Chaos, Solitons and Fractals 34 (2007) 1636--1648.

A Stage-Structured Predator-Prey System with Time Delay and Beddington-DeAngelis Functional Response

A stage-structured predator-prey system with time delay and Beddington- DeAngelis functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.