Bifurcation Analysis in a Delay Differential Equations, which Confers a Strong Allee Effect in Escherichia Coli
| Autor: | Qiubao Wang, Ruilan Tian |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Mathematical Modelling and Analysis, Vol 20, Iss 6 (2015) |
| Druh dokumentu: | article |
| ISSN: | 13926292 1392-6292 1648-3510 |
| DOI: | 10.3846/13926292.2015.1113206 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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