Melnikov method to a bacteria-immunity model with bacterial quorum sensing mechanism.

*(English)*Zbl 1197.37130Summary: A bacteria-immunity model with bacterial quorum sensing is formulated, which describes the competition between bacteria and immune cells. After periodic perturbation and a series of coordinate transformations, the model is brought into a standard form, and which is amenable to Melnikov method. By the method, the existences of chaotic motion and homoclinic bifurcations are proved.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

PDF
BibTeX
XML
Cite

\textit{Z. Zhang} et al., Chaos Solitons Fractals 40, No. 1, 414--420 (2009; Zbl 1197.37130)

Full Text:
DOI

##### References:

[1] | Medzhitov, R.; Janeway, C.A., Innate immune recognition and control of adaptive immune responses, Sem immunol, 10, 351-353, (1998) |

[2] | Levy, J.A., The importance of the innate immune system in controlling HIV infection and disease, Trends immunol, 22, 312-316, (2001) |

[3] | Henke, J.M.; Bassler, B.L., Bacterial social engagements, Trends cell biol, 14, 648-656, (2004) |

[4] | Nealson, K.H.; Platt, T.; Hastings, J.W., Cellular control of the synthesis and activity of the bacterial luminescent system, J bacteriol, 104, 313-322, (1970) |

[5] | Eberhard, A., Inhibition and activation of bacterial luciferase synthesis, J bacteriol, 109, 1101-1105, (1972) |

[6] | Chacón, R., Reshaping-induced spatiotemporal chaos in driver damped sine – gordon systems, Chaos, solitons & fractals, 31, 1265-1271, (2007) |

[7] | Huang, D.W., On chaotic motion of some stochastic nonlinear dynamic system, Chaos, solitons & fractals, 31, 242-246, (2007) |

[8] | Baesens, N.C.; Nicolis, G., Complex bifurcations in a periodically forced normal form, Z phys B, 52, 345-354, (1983) |

[9] | Glendinning, P.; Perry, L.P., Melnikov analysis of chaos in a simple epidemiological model, J math biol, 34, 359-373, (1997) · Zbl 0867.92021 |

[10] | Ravichanndran, V.; Chinnathambi, V.; Rajasekar, S., Homoclinic bifurcation and chaos in Duffing oscillator driven by an amplitude-modulated forced, Physica A, 376, 223-236, (2007) |

[11] | Wu, Z.; Xie, J.; Fang, Y.; Xu, Z., Controlling chaos with periodic parameterize perturbations in Lorenz system, Chaos, solitons & fractals, 32, 104-112, (2007) · Zbl 1138.37314 |

[12] | Wang, K.F.; Wang, W.D.; Liu, X.N., Viral infection model with periodic lytic immune response, Chaos, solitons & fractals, 28, 90-99, (2006) · Zbl 1079.92048 |

[13] | Gutnikov, S.; Melnikov, Y., A simple non-linear model of immune response, Chaos, solitons & fractals, 16, 125-132, (2003) · Zbl 1032.92008 |

[14] | Zhang J, Cerasuolo M, Fergola P, Ma Z. On the influence of quorum sensing in the competition between bacteria and immune system, in press. |

[15] | Guckenheimer, J.; Holmes, P., Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, (1983), Springer New York · Zbl 0515.34001 |

[16] | Wiggins, S., Global bifurcations and chaos, (1988), Springer New York · Zbl 0661.58001 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.