Displaying similar documents to “Nutrient-phytoplankton-zooplankton interaction with variable yields”

Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

Changjin Xu, Maoxin Liao, Xiaofei He (2011)

International Journal of Applied Mathematics and Computer Science

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In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical...

Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System

J.-C. Poggiale, M. Gauduchon, P. Auger (2008)

Mathematical Modelling of Natural Phenomena

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This paper is devoted to the study of a predator-prey model in a patchy environment. The model represents the interactions between phytoplankton and zooplankton in the water column. Two patches are considered with respect to light availability: one patch is associated to the surface layer, the second patch describes the bottom layer. We show that this spatial heterogeneity may destabilize the predator-prey system, even in oligotrophic system where the nutrient is low enough to avoid...

Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response

Qiaoling Chen, Zhidong Teng, Zengyun Hu (2013)

International Journal of Applied Mathematics and Computer Science

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The dynamics of a discrete-time predator-prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations...

Persistence and bifurcation analysis on a predator–prey system of holling type

Debasis Mukherjee (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation.

Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion

Kousuke Kuto, Yoshio Yamada (2004)

Banach Center Publications

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This article discusses a prey-predator system with cross-diffusion. We obtain multiple positive steady-state solutions of this system. More precisely, we prove that the set of positive steady-states possibly contains an S or ⊃-shaped branch with respect to a bifurcation parameter in the large cross-diffusion case. Next we give some criteria on the stability of these positive steady-states. Furthermore, we find the Hopf bifurcation point on the steady-state solution branch in a certain...

Persistence and bifurcation analysis on a predator–prey system of holling type

Debasis Mukherjee (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation.