Dynamics of stochastic diffusive coral reef ecosystems with Lévy noise

Zaitang Huang; Zhiye Zhong; Yousu Huang; Yumei Lu; Zaitang Huang; Zhiye Zhong; Yousu Huang; Yumei Lu

doi:10.3934/mbe.2025080

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 8: 2176-2212. doi: 10.3934/mbe.2025080

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Dynamics of stochastic diffusive coral reef ecosystems with Lévy noise

1.
School of Mathematics and Statistics, Nanning Normal University, Nanning 530023, China
2.
Center for Applied Mathematics of Guangxi, Nanning Normal University, Nanning 530023, China

Received: 19 December 2024 Revised: 11 June 2025 Accepted: 19 June 2025 Published: 10 July 2025

This paper was mainly concerned with the asymptotic dynamics of stochastic diffusive coral reef ecosystems with Lévy noise. First, we proved the well-posedness and energy estimates of solution. Second, under some suitable conditions, we proved the existence and uniqueness of weak pullback mean random attractors and invariant measures. Finally, a large deviation principle result for solutions of stochastic diffusive coral reef ecosystems with Lévy noise was obtained by a variational formula for positive functionals of a Poisson random measure and the method of weak convergence. Interestingly, this showed the effect of Lévy noise which can stabilize or destabilize systems, which was significantly different from the classical Brownian motion process.
- stochastic diffusive coral reef model,
- existence results,
- weak attractors,
- invariant measures,
- large deviation result
Citation: Zaitang Huang, Zhiye Zhong, Yousu Huang, Yumei Lu. Dynamics of stochastic diffusive coral reef ecosystems with Lévy noise[J]. Mathematical Biosciences and Engineering, 2025, 22(8): 2176-2212. doi: 10.3934/mbe.2025080

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Abstract

This paper was mainly concerned with the asymptotic dynamics of stochastic diffusive coral reef ecosystems with Lévy noise. First, we proved the well-posedness and energy estimates of solution. Second, under some suitable conditions, we proved the existence and uniqueness of weak pullback mean random attractors and invariant measures. Finally, a large deviation principle result for solutions of stochastic diffusive coral reef ecosystems with Lévy noise was obtained by a variational formula for positive functionals of a Poisson random measure and the method of weak convergence. Interestingly, this showed the effect of Lévy noise which can stabilize or destabilize systems, which was significantly different from the classical Brownian motion process.

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