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Lévy noise influences basin stability in a delayed vegetation-water dynamical system
1Department of Mathematics, Xi'an University of Science and Technology, Xi'an 710054, People's Republic of China.
Chaos (Woodbury, N.Y.)
|April 25, 2023
Summary
This study explores stochastic stability in a time-delayed vegetation-water ecosystem with Lévy noise. Time delays can alleviate instability caused by noise intensity, enhancing ecosystem resilience.
Area of Science:
- Ecology
- Environmental Science
- Mathematical Biology
Background:
- Ecosystems are complex and influenced by environmental stochasticity.
- Time delays are critical factors in ecological dynamics.
- Lévy noise introduces unique stochastic perturbations.
Purpose of the Study:
- To investigate the stochastic stability of a time-delayed vegetation-water ecosystem under Lévy noise.
- To analyze the impact of noise intensity and time delay on ecosystem stability.
- To define and assess metastable basins using statistical indicators.
Main Methods:
- Modeling a time-delayed vegetation-water ecosystem with Lévy noise.
- Utilizing statistical indicators: First Escape Probability (FEP) and Mean First Exit Time (MFET).
- Implementing a numerical algorithm for FEP and MFET calculation, verified by Monte Carlo simulations.
Main Results:
- Average time delay affects attraction basins but not attractors.
- Noise intensity decreases vegetation biomass basin stability.
- Time delay can mitigate instability caused by stochastic noise.
Conclusions:
- The study quantifies stochastic stability in a complex ecological model.
- FEP and MFET are consistent indicators for assessing metastable basins.
- Time delays offer a potential mechanism for enhancing ecosystem resilience against stochastic disturbances.
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