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Structure analysis of the attracting sets for plankton models driven by bounded noises
1School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, China.
Mathematical Biosciences and Engineering : MBE
|May 10, 2023
Summary
This study proves the existence of attracting sets for plankton models with bounded noise, offering conditions for species survival in fluctuating environments.
Area of Science:
- Mathematical Biology
- Dynamical Systems
- Stochastic Processes
Background:
- Plankton population dynamics are crucial for aquatic ecosystems.
- Environmental fluctuations can significantly impact species survival.
- Stochastic differential equations are used to model environmental noise.
Purpose of the Study:
- To investigate the existence and uniqueness of solutions for plankton models with Ornstein-Uhlenbeck noise.
- To establish the existence of attracting sets for the generated random dynamical systems.
- To determine conditions for plankton species persistence and extinction.
Main Methods:
- Analysis of random dynamical systems.
- Proof of existence and uniqueness of solutions for stochastic models.
- Investigation of the internal structure of attracting sets.
- Derivation of sufficient conditions for species persistence and extinction.
Main Results:
- Existence and uniqueness of solutions for the perturbed plankton models are proven.
- The existence of attracting sets for the random dynamical systems is established.
- Sufficient conditions for plankton species persistence and extinction in fluctuating environments are derived.
Conclusions:
- The study provides a rigorous mathematical framework for understanding plankton dynamics under environmental noise.
- The results offer insights into the factors governing the survival or extinction of plankton species.
- Numerical simulations support the theoretical findings on attracting sets and species persistence.
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