Related papers: A study on a class of predator-prey models with Al…
In this paper, we discuss a hierarchical model, based on a Ricker competition model. The species considered are competing for resources and may be subject to an Allee effect due to mate limitation, anti-predator vigilance or aggression,…
In this paper, we develop a method of analyzing long transient dynamics in a class of predator-prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the…
We examine the interaction of transcritical and saddle-node bifurcations in a predator-prey-nutrient system that is stressed by the presence of a toxicant affecting the prey. This model, formulated by Kooi et al. ({\sl Ecol. Model.} {\bf…
The dynamics of a prey-predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root…
Over the last few decades, complex oscillations of slow-fast systems have been a key area of research. In the theory of slow-fast systems, the location of singular Hopf bifurcation and maximal canard is determined by computing the first…
We perform dynamical analysis on a stochastic Rosenzweig-MacArthur model driven by {\alpha}-stable L\'evy motion. We analyze the existence of the equilibrium points, and provide a clear illustration of their stability. It is shown that the…
The Allee effect describes a decline in population fitness at low densities, potentially leading to extinction. In predator-prey systems, an emergent Allee effect can arise due to interactions such as density-dependent maturation rates and…
We explore a diffusive predator-prey system that incorporates the fear effect in advective environments. Firstly, we analyze the eigenvalue problem and the adjoint operator, considering Constant-Flux and Dirichlet (CF/D) boundary…
Recently, research on the complex periodic behavior of multi-scale systems has become increasingly popular. Krupa et al. \cite{krupa2} provided a way to obtain relaxation oscillations in slow-fast systems through singular Hopf bifurcations…
A new model to investigate environmental effects of genetically distinguishable predators is presented. The Holling type II response function, modelling feeding satiation, leads to persistent system's oscillations, as in classical…
We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of prey-predator system is apparent rather than real and there are still many of its hidden properties that have been…
The population dynamics of predator-prey systems in the presence of patch-specific predators are explored in a setting where the prey population has access to both habitats. The emphasis is in situations where patch-prey abundance drives…
The Allee effect is an important phenomenon in population biology characterized by positive density dependence, that is a positive correlation between population density and individual fitness. However, the effect is not well studied in…
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…
The predator-prey dynamic appertaining to two species is explored, wherein the predator species is structured into different stages. As evidenced from natural documentation, the immature predators possess the potential to predate albeit not…
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…
In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated…
We study a fast-slow version of the Bazykin-Berezovskaya predator-prey model with Allee effect evolving on two timescales, through the lenses of Geometric Singular Perturbation Theory (GSPT). The system we consider is in non-standard form.…
The search for more realistic models for interacting species has produced many adaptations of the original Lotka-Volterra equations, such as the inclusion of the Allee effect and the different Holling's types of functional response. In the…