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Bifurcation and complexity in a ratio-dependent predator-prey chemostat with pulsed input

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Abstract

In this paper, a three dimensional ratio-dependent chemostat model with periodically pulsed input is considered. By using the discrete dynamical system determined by the stroboscopic map and Floquet theorem, an exact periodic solution with positive concentrations of substrate and predator in the absence of prey is obtained. When β is less than some critical value the boundary periodic solution (x s (t), 0, z s (t)) is locally stable, and when β is larger than the critical value there are periodic oscillations in substrate, prey and predator. Increasing the impulsive period τ, the system undergoes a series of period-doubling bifurcation leading to chaos, which implies that the dynamical behaviors of the periodically pulsed ratio-dependent predator-prey ecosystem are very complex.

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Authors and Affiliations

  1. Dept. of Appl. Math., Dalian Univ. of Tech., Dalian, 116024, China

    Zhao Zhong

  2. Dept. of Math., Huanghuai College, Zhumadian, 463000, China

    Zhao Zhong

  3. Dept. of Math., Xinyan Normal Univ., Henan, 464000, China

    Song Xinyu

Authors
  1. Zhao Zhong
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  2. Song Xinyu
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Supported by the National Natural Science Foundation of China (10471117), the Henan Innovation Project for University Prominent Research Talents(2005KYCX017) and the Scientific Research Foundation of Education Ministry for the Returned Overseas Chinese Scholars.

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Zhao, Z., Song, X. Bifurcation and complexity in a ratio-dependent predator-prey chemostat with pulsed input. Appl. Math.- J. Chin. Univ. 22, 379–387 (2007). https://doi.org/10.1007/s11766-007-0401-4

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  • DOI: https://doi.org/10.1007/s11766-007-0401-4

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