Modeling herd behavior in population systems

V Ajraldi, M Pittavino, E Venturino - Nonlinear Analysis: Real World …, 2011 - Elsevier
In this paper, we show that under suitable simple assumptions the classical two populations
system may exhibit unexpected behaviors. Considering a more elaborated social model, in …

Predator–prey system with strong Allee effect in prey

J Wang, J Shi, J Wei - Journal of Mathematical Biology, 2011 - Springer
Global bifurcation analysis of a class of general predator–prey models with a strong Allee
effect in prey population is given in details. We show the existence of a point-to-point …

Global dynamics of a ratio-dependent predator-prey system

D Xiao, S Ruan - Journal of Mathematical Biology, 2001 - Springer
Recently, ratio-dependent predator-prey systems have been regarded by some researchers
to be more appropriate for predator-prey interactions where predation involves serious …

Bifurcation analysis of a ratio-dependent prey–predator model with the Allee effect

M Sen, M Banerjee, A Morozov - Ecological Complexity, 2012 - Elsevier
There is a growing body of evidence supporting implementation of ratio-dependent
functional response of predators in ecological models. Those models often provide a …

Role of fear in a predator-prey system with ratio-dependent functional response in deterministic and stochastic environment

J Roy, D Barman, S Alam - Biosystems, 2020 - Elsevier
In this article, we propose and analyse a predator-prey model where apart from direct
predation the prey population is affected by the fear induced from predators. The …

Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting

D Xiao, LS Jennings - SIAM Journal on Applied Mathematics, 2005 - SIAM
The ratio-dependent predator-prey model exhibits rich interesting dynamics due to the
singularity of the origin. The objective of this paper is to study the dynamical properties of the …

Bifurcation analysis of the predator–prey model with the Allee effect in the predator

D Sen, S Ghorai, M Banerjee, A Morozov - Journal of mathematical biology, 2022 - Springer
The use of predator–prey models in theoretical ecology has a long history, and the model
equations have largely evolved since the original Lotka–Volterra system towards more …

Global analysis of the predator–prey system with Beddington–DeAngelis functional response

TW Hwang - Journal of Mathematical Analysis and Applications, 2003 - Elsevier
Global analysis of the predator–prey system with Beddington–DeAngelis functional response
Page 1 J. Math. Anal. Appl. 281 (2003) 395–401 www.elsevier.com/locate/jmaa Note Global …

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

M Fan, Y Kuang - Journal of Mathematical Analysis and applications, 2004 - Elsevier
In this paper, we systematically study the dynamics of a nonautonomous predator–prey
system with the Beddington–DeAngelis functional response. The explorations involve the …

Ratio-dependent predator–prey model: effect of environmental fluctuation and stability

M Bandyopadhyay, J Chattopadhyay - Nonlinearity, 2005 - iopscience.iop.org
This paper deals with the problem of a ratio-dependent predator–prey model. The
deterministic and stochastic behaviour of the model system around biologically feasible …