Bifurcation and chaotic behavior in stochastic Rosenzweig–MacArthur prey–predator model with non-Gaussian stable Lévy noise

Yuan, Shenglan; Wang, Xiao

doi:10.1016/j.ijnonlinmec.2022.104339

Cited by 5 publications

(2 citation statements)

References 15 publications

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“…The population may be affected by sudden environmental noise [16,17]. For example, earthquakes [18], changes in temperature [19], and hurricanes [20] can be appropriately modeled as random fluctuations or stochastic events, as their occurrence and impact are less predictable and more influenced by stochasticity. These sudden environmental perturbations may bring substantial social and economic losses.…”

Section: Introductionmentioning

confidence: 99%

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise

Abebe,

Yuan,

Tesfay

et al. 2024

Mathematics

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We explore the most probable phase portrait (MPPP) of a stochastic single-species model incorporating the Allee effect by utilizing the nonlocal Fokker–Planck equation (FPE). This stochastic model incorporates both non-Gaussian and Gaussian noise sources. It has three fixed points in the deterministic case. One is the unstable state, which lies between the two stable equilibria. Our primary focus is on elucidating the transition pathways from extinction to the upper stable state in this single-species model, particularly under the influence of jump-diffusion noise. This helps us to study the biological behavior of species. The identification of the most probable path relies on solving the nonlocal FPE tailored to the population dynamics of the single-species model. This enables us to pinpoint the corresponding maximum possible stable equilibrium state. Additionally, we derive the Onsager–Machlup function for the stochastic model and employ it to determine the corresponding most probable paths. Numerical simulations manifest three key insights: (i) when non-Gaussian noise is present in the system, the peak of the stationary density function aligns with the most probable stable equilibrium state; (ii) if the initial value rises from extinction to the upper stable state, then the most probable trajectory converges towards the maximally probable equilibrium state, situated approximately between 9 and 10; and (iii) the most probable paths exhibit a rapid ascent towards the stable state, then maintain a sustained near-constant level, gradually approaching the upper stable equilibrium as time goes on. These numerical findings pave the way for further experimental investigations aiming to deepen our comprehension of dynamical systems within the context of biological modeling.

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Section: Introductionmentioning

confidence: 99%

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise

Abebe,

Yuan,

Tesfay

et al. 2024

Mathematics

Self Cite

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“…The population may be affected by sudden environmental noises [34,53]. For example, severe acute respiratory syndrome (SARS), human immunodeficiency virus (HIV), the smoking habit [59], and the recent Coronavirus [44], earthquakes [52], temperature [55], and hurricanes [51]. These sudden environmental perturbations may bring substantial social and economic losses.…”

Section: Introductionmentioning

confidence: 99%

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise

Tesfay,

Yuan,

Tesfay

et al. 2023

Preprint

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We investigate the most probable phase portrait (MPPP) of a stochastic single-species model with the Alleeeffect using the non-local Fokker-Planck equation (FPE). This stochastic model is driven by non-Gaussianas well as Gaussian noise. It has three fixed points in the deterministic case. One of them is the unstablestate which lies between the two stable equilibria. We focus on the transition pathways from the extinctionstate to the upper fixed stable state for the transcription factor activator in a single-species model. This helpsus to study the biological behavior of species. The most probable path is obtained from the solution of thenon-local Fokker-Planck equation corresponding to the population system of the single-species model, andthe corresponding maximum possible stable equilibrium state is determined. We also acquire the Onsager-Machlup function for the stochastic model and solve the corresponding most probable paths. The numericalsimulation manifests that: (i) When non-Gaussian noise is presented in the system, the maximum of thestationary density function is located at the most probable stable equilibrium state; (ii) If the initial valueincreases from extinction state to the upper stable state, the most probable trajectory goes to the maximallikely equilibrium state, in our case it lies between 9 and 10; (iii) The most probable paths increase to stablestate quickly, then maintain a nearly constant level, and approach to the upper stable equilibrium state astime goes on. These numerical experiment findings accelerate growth for further experimental study, inorder to achieve good knowledge about dynamical systems in biology. 2020 MSC: 39A50, 45K05, 65N12

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Stationary distribution and mean extinction time in a generalist prey–predator model driven by Lévy noises

Zhuo,

Guo,

et al. 2024

Chaos, Solitons & Fractals

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Bifurcation and chaotic behavior in stochastic Rosenzweig–MacArthur prey–predator model with non-Gaussian stable Lévy noise

Cited by 5 publications

References 15 publications

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise

Most Probable Dynamics of the Single-Species with Allee Effect under Jump-Diffusion Noise

Stationary distribution and mean extinction time in a generalist prey–predator model driven by Lévy noises

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