Related papers: Stability of a Delayed Predator-Prey Model for Pum…
Following the well-extablished mathematical approach to persistence and its recent developments we give a rigorous theoretical explanation to the numerical results obtained for a certain prey-predator model with functional response of…
This paper investigates a dynamical predator-prey interaction model that incorporates: (a) hunting cooperation among predators; (b) Allee effect in prey. We show all possible boundary and interior solutions. In order to analyze the…
Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey-predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than…
Ratio-dependent predator-prey models have been increasingly favored by field ecologists where predator-prey interactions have to be taken into account the process of predation search. In this paper we study the conditions of the existence…
Our study focuses on analyzing the behavior of a stochastic predator-prey model with a time delay and logistic growth of prey, influenced by L\'{e}vy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive…
A delayed, discrete-time, prey-predator model with Allee effects imposed on prey and predator populations is defined, and dynamics of the system is characterized computationally. The parametric conditions for local asymptotic stability of…
In this article, a Leslie-Gower Holling type III predator-prey model with disease in predator has been developed from both biological and mathematical point of view. The total population is divided into three classes, namely, prey,…
This paper deals with ratio-dependent predator-prey systems with delay. We will investigate under what conditions delay cannot cause instability in higher dimension. We give an example when delay causes instability.
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…
Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka-Volterra model which defined the interaction between predator and prey…
Generalist predators consist an important component of an ecosystem which may act as a biocontrol agent and influence the dynamics significantly. In this paper, we have studied the effect of delayed logistic growth of the prey species with…
We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the…
Cannibalism, which is the act of killing and at least partial consumption of conspecifics, is ubiquitous in nature. Mathematical models have considered cannibalism in the predator primarily, and show that predator cannibalism in two species…
In this manuscript, we consider temporal and spatio-temporal modified Holling-Tanner predator-prey models with predator-prey growth rate as a logistic type, Holling type II functional response and alternative food sources for the predator.…
The time-global unique solvability on the reaction diffusion equations for prey-predator models with density-dependent inhibitor and dormancy on predators is established. The crucial step of the proof is to construct time-local non-negative…
A general framework for age-structured predator-prey systems is introduced. Individuals are distinguished into two classes, juveniles and adults, and several possible interactions are considered. The initial system of partial differential…
A cubic discrete coupled logistic equation is proposed to model the predator-prey problem. The coupling depends on the population size of both species and on a positive constant $\lambda$, which could depend on the prey reproduction rate…
Switching model with one predator and two prey species is considered. The prey species have the ability of group defence. Therefore, the predator will be attracted towards that habitat where prey are less in number. The stability analysis…
In this study, we investigate a prey-predator model exhibiting Holling type-III functional response among mutually interfering predators to assess the effects of provision of additional food to natural enemies in altering pest dynamics. We…