Open AccessBIFURCATION ANALYSIS IN A DELAY DIFFERENTIAL EQUATIONS, WHICH CONFERS A STRONG ALLEE EFFECT IN ESCHERICHIA COLI
Author(s) -
Qiubao Wang,
Ruilan Tian
Publication year - 2015
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2015.1113206
Subject(s) - allee effect , mathematics , center manifold , bifurcation diagram , hopf bifurcation , bifurcation , saddle node bifurcation , delay differential equation , pitchfork bifurcation , mathematical analysis , torus , differential equation , geometry , physics , nonlinear system , population , demography , quantum mechanics , sociology
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.