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Determination of the Settling Rate of Clay/Cyanobacterial Floccules
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DYNAMICS OF STOCHASTIC MICROORGANISM FLOCCULATION MODELS.

Alexandru Hening1, Nguyen T Hieu2, Dang H Nguyen3

  • 1Department of Mathematics, Texas A&M University, Mailstop 3368, College Station, TX 77843-3368, United States.

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|December 3, 2025
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Summary
This summary is machine-generated.

This study introduces a novel stochastic model for microorganism flocculation, accounting for environmental shifts. Researchers developed new techniques to classify the models

Keywords:
ergodicityextinctionflocculation modelinvariant measurespersistenceswitching diffusion

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Stochastic Processes

Background:

  • Microorganism flocculation is influenced by environmental and seasonal fluctuations.
  • Existing models may not fully capture the complex dynamics of these fluctuations.

Purpose of the Study:

  • To propose a stochastic model incorporating multiple layers of stochasticity for microorganism flocculation.
  • To analyze the asymptotic behavior and classify the persistence and extinction of the process.

Main Methods:

  • Development of a novel stochastic model with multi-layered stochasticity.
  • Application of new analytical techniques to address non-Kolmogorov systems.
  • Classification of the asymptotic behavior of the proposed model.

Main Results:

  • A full classification of the asymptotic behavior of the stochastic microorganism flocculation model was achieved.
  • New mathematical techniques were successfully developed to analyze the system's persistence and extinction.

Conclusions:

  • The proposed multi-layered stochastic model provides a more comprehensive understanding of microorganism flocculation dynamics.
  • The developed analytical methods are crucial for studying complex, non-Kolmogorov stochastic systems.