Threshold analysis of an algae-zooplankton model incorporating general interaction rates and nonlinear independent stochastic components

Yassine Sabbar; Aeshah A. Raezah; Yassine Sabbar; Aeshah A. Raezah

doi:10.3934/math.2024889

AIMS Mathematics

2024, Volume 9, Issue 7: 18211-18235. doi: 10.3934/math.2024889

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Threshold analysis of an algae-zooplankton model incorporating general interaction rates and nonlinear independent stochastic components

Yassine Sabbar ^{1
,
,},
Aeshah A. Raezah ²

1.
MAIS Laboratory, MAMCS Group, FST Errachidia, Moulay Ismail University of Meknes, P.O. Box 509, Errachidia 52000, Morocco
2.
Department of Mathematics, Faculty of Science King Khalid, University Abha, 62529, Saudi Arabia

Received: 27 March 2024 Revised: 23 May 2024 Accepted: 27 May 2024 Published: 29 May 2024
MSC : 37A50

The stochastic nature of ecological systems is fundamental to their modeling and understanding. In this paper, we introduce a comprehensive algae-zooplankton model that incorporates general interaction rate and second-order independent stochastic components. Our model's perturbation component encompasses both white noise and jump processes, enabling us to account for various sources of variability and capture a wide range of potential fluctuations in the system. By utilizing an auxiliary equation, we establish a global threshold for the stochastic system, distinguishing between scenarios of extinction and ergodicity. This threshold serves as a critical determinant of the system's long-term behavior and sheds light on the delicate balance between population persistence and decline in ecological communities. To elucidate the impact of noise on the dynamics of algae and zooplankton, we present a series of numerical illustrations. Through these simulations, we highlight how noise influences not only the extinction time but also the shape of the stationary distribution. Our findings underscore the significant role of stochasticity in shaping ecological dynamics and emphasize the importance of considering noise effects in ecological modeling and management practices.
- algae,
- zooplankton,
- Lévy noise,
- Brownian motion,
- jumps,
- dynamics
Citation: Yassine Sabbar, Aeshah A. Raezah. Threshold analysis of an algae-zooplankton model incorporating general interaction rates and nonlinear independent stochastic components[J]. AIMS Mathematics, 2024, 9(7): 18211-18235. doi: 10.3934/math.2024889

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Abstract

The stochastic nature of ecological systems is fundamental to their modeling and understanding. In this paper, we introduce a comprehensive algae-zooplankton model that incorporates general interaction rate and second-order independent stochastic components. Our model's perturbation component encompasses both white noise and jump processes, enabling us to account for various sources of variability and capture a wide range of potential fluctuations in the system. By utilizing an auxiliary equation, we establish a global threshold for the stochastic system, distinguishing between scenarios of extinction and ergodicity. This threshold serves as a critical determinant of the system's long-term behavior and sheds light on the delicate balance between population persistence and decline in ecological communities. To elucidate the impact of noise on the dynamics of algae and zooplankton, we present a series of numerical illustrations. Through these simulations, we highlight how noise influences not only the extinction time but also the shape of the stationary distribution. Our findings underscore the significant role of stochasticity in shaping ecological dynamics and emphasize the importance of considering noise effects in ecological modeling and management practices.

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