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Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics

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  • Huang, Dongwei
  • Wang, Hongli
  • Feng, Jianfeng
  • Zhu, Zhi-wen

Abstract

A nonlinear stochastic dynamical model on a typical HAB algae diatom and dianoflagellate densities was created and presented in this paper. Simplifying the model through a stochastic averaging method, we obtained a two-dimensional diffusion process of averaged amplitude and phase. The singular boundary theory of diffusion process and the invariant measure theory were applied in analyzing the bifurcation of stability and the Hopf bifurcation of the stochastic system. The critical value of the stochastic Hopf bifurcation parameter was obtained and the conclusion that the position of Hopf bifurcation drifting with the parameter increase is presented as a result.

Suggested Citation

  • Huang, Dongwei & Wang, Hongli & Feng, Jianfeng & Zhu, Zhi-wen, 2006. "Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1072-1079.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:1072-1079
    DOI: 10.1016/j.chaos.2005.04.086
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    1. Spagnolo, B. & La Barbera, A., 2002. "Role of the noise on the transient dynamics of an ecosystem of interacting species," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 114-124.
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    2. Huang, Zaitang & Yang, Qigui & Cao, Junfei, 2011. "Complex dynamics in a stochastic internal HIV model," Chaos, Solitons & Fractals, Elsevier, vol. 44(11), pages 954-963.
    3. Zhang, Yue & Zheng, Yan & Liu, Xi & Zhang, Qingling & Li, Aihua, 2016. "Dynamical analysis of a differential algebraic bio-economic model with stage-structured and stochastic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 222-229.
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