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

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  • Zhang, Zhonghua
  • Peng, Jigen
  • Zhang, Juan

Abstract

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.

Suggested Citation

  • Zhang, Zhonghua & Peng, Jigen & Zhang, Juan, 2009. "Melnikov method to a bacteria-immunity model with bacterial quorum sensing mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 414-420.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:1:p:414-420
    DOI: 10.1016/j.chaos.2007.07.079
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    References listed on IDEAS

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    1. Ravichandran, V. & Chinnathambi, V. & Rajasekar, S., 2007. "Homoclinic bifurcation and chaos in Duffing oscillator driven by an amplitude-modulated force," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 223-236.
    2. Huang, Dong-Wei & Gao, Qin & Wang, Hong-Li & Feng, Jian-Feng & Zhu, Zhi-Wen, 2007. "On chaotic motion of some stochastic nonlinear dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 242-246.
    3. Wang, Kaifa & Wang, Wendi & Liu, Xianning, 2006. "Viral infection model with periodic lytic immune response," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 90-99.
    4. Wu, Zhengmao & Xie, Jianying & Fang, Yanyan & Xu, Zhenyuan, 2007. "Controlling chaos with periodic parametric perturbations in Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 104-112.
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