Global dynamics of a three-species spatial food chain model

HY Jin, ZA Wang, L Wu - Journal of Differential Equations, 2022 - Elsevier
In this paper, we study the following initial-boundary value problem of a three-species
spatial food chain model {ut= d 1 Δ u+ u (1− u)− b 1 uv, x∈ Ω, t> 0 vt= d 2 Δ v−∇⋅(ξ v∇ u)+ …

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 dynamics with square root functional responses

PA Braza - Nonlinear Analysis: Real World Applications, 2012 - Elsevier
A predator–prey model is considered in which a modified Lotka–Volterra interaction term is
used as the functional response of the predator to the prey. The interaction term is …

Ratio-dependent predator-prey models of interacting populations

M Haque - Bulletin of mathematical biology, 2009 - Springer
Ratio-dependent predator-prey models are increasingly favored by both the theoretical and
experimental ecologists as a more suitable alternative to describe predator-prey interactions …

Dynamical behavior of fractional-order Hastings–Powell food chain model and its discretization

AE Matouk, AA Elsadany, E Ahmed… - … in Nonlinear Science and …, 2015 - Elsevier
In this work, the dynamical behavior of fractional-order Hastings–Powell food chain model is
investigated and a new discretization method of the fractional-order system is introduced. A …

Infection in prey population may act as a biological control in ratio-dependent predator–prey models

O Arino, J Mikram, J Chattopadhyay - Nonlinearity, 2004 - iopscience.iop.org
A ratio-dependent predator–prey model with infection in prey population is proposed and
analysed. The behaviour of the system near the biological feasible equilibria is observed …

An ecoepidemiological model with disease in predator: the ratio‐dependent case

M Haque, E Venturino - Mathematical methods in the Applied …, 2007 - Wiley Online Library
We propose a ratio‐dependent demographic predator–prey model in which also a disease
spreads among predators via homogeneous mixing. Equilibria of the system are analysed …

Dynamic behaviour of a reaction–diffusion predator–prey model with both refuge and harvesting

LN Guin, S Acharya - Nonlinear Dynamics, 2017 - Springer
An appropriate mathematical structure to describe the population dynamics is given by the
partial differential equations of reaction–diffusion type. The spatiotemporal dynamics and …

Stationary patterns for a prey–predator model with prey-dependent and ratio-dependent functional responses and diffusion

M Wang - Physica D: Nonlinear Phenomena, 2004 - Elsevier
We study a reaction diffusion system arising from a three-species prey–predator model with
prey-dependent and ratio-dependent functional responses. The main aim of this paper is to …

Shape effects on herd behavior in ecological interacting population models

IM Bulai, E Venturino - Mathematics and Computers in Simulation, 2017 - Elsevier
In this paper, we introduce several dynamical systems modeling two-populations
interactions. The main idea is to assume that the individuals of one of the populations gather …