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Bifurcation Analysis in a Delay Differential Equations, which Confers a Strong Allee Effect in Escherichia Coli

    Qiubao Wang Affiliation
    ; Ruilan Tian Affiliation

Abstract

The paper addresses the bifurcations for a delay differential model with parameters which confers a strong Allee effect in Escherichia coli. Stability and local Hopf bifurcations are analyzed when the delay τ or σ as parameter. It is also found that there is a non-resonant double Hopf bifurcation occur due to the vanishing of the real parts of two pairs of characteristic roots. We transform the original system into a finite dimensional system by the center manifold theory and simplify the system further by the normal form method. Then, we obtain a complete bifurcation diagram of the system. Finally, we provide numerical results to illustrate our conclusions. There are many interesting phenomena, such as attractive quasi-periodic solution and three-dimensional invariant torus.

Keyword : double Hopf, bifurcation, delay, center manifold

How to Cite
Wang, Q., & Tian, R. (2015). Bifurcation Analysis in a Delay Differential Equations, which Confers a Strong Allee Effect in Escherichia Coli. Mathematical Modelling and Analysis, 20(6), 782-801. https://doi.org/10.3846/13926292.2015.1113206
Published in Issue
Nov 23, 2015
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This work is licensed under a Creative Commons Attribution 4.0 International License.