Dynamics of a nonautonomous predator–prey system with the Beddington–DeAngelis functional response

Abstract

In this paper, we systematically study the dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response. The explorations involve the permanence, extinction, global asymptotic stability (general nonautonomous case); the existence, uniqueness and stability of a positive (almost) periodic solution and a boundary (almost) periodic solution for the periodic (almost periodic) case. The paper ends with some interesting numerical simulations that complement our analytical findings.  2004 Elsevier Inc. All rights reserved.

Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

“…It is well known that the functional response plays important role in the predator-prey model, and during the past two decades, the Beddington-DeAngelis functional response, which is a combination of the famous Holling II functional response and ratio-dependent functional response, having overcome the defect of the both functional response, is studied by many scholars, see [26][27][28][29][30] and the references therein.…”

“…The success of [26][27][28][29][30] motivated us to propose the competition system with Beddington-DeAngelis functional response, also, if we further assume that each species produces a substance toxic to the other only when the other is present, or assume that one species is toxic produce while the other one is non-toxic producing, then, we could establish the model (1) and (2), respectively. It is, to the best of the knowledge of the authors, the first time such kind of model proposed.…”

Mathematical Model for Two-Spotted Spider Mites System: Verification and Validation

“…However, researchers have argued that when predators must search for food and then share or compete for food, the functional response should depend on both prey and predator densities. Considerable evidence suggests that predator-dependent functional responses occur quite frequently in laboratory as well as in natural systems [10]. One of the most popular functional responses is the Beddington-DeAngelis functional response [11] [12], originally proposed by Beddington [13] and DeAngelis et al [14].…”

Dynamics of a Discrete Ratio-Dependent Predator-Prey System Incorporating Harvesting

“…In population dynamics, a number of continuous-time systems of predator-prey type have been investigated by many researchers for several decades (see [2,6,8,9,10,11,13,15,16,17,18,19]). However, sometimes it is useful to consider discrete-time systems described by difference equations, discrete dynamical systems or iterative maps.…”