# Stochastic bifurcation in single-species model induced by α-stable Lévy noise

@article{Tesfay2020StochasticBI, title={Stochastic bifurcation in single-species model induced by $\alpha$-stable L{\'e}vy noise}, author={Almaz Tesfay and Daniel Tesfay and Shenglan Yuan and James Ryan Brannan and Jinqiao Duan}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2020}, volume={2021} }

Bifurcation analysis has many applications in different scientific fields, such as electronics, biology, ecology, and economics. In population biology, deterministic methods of bifurcation are commonly used. In contrast, stochastic bifurcation techniques are infrequently employed. Here we establish stochastic P-bifurcation behavior of (i) a growth model with state dependent birth rate and constant death rate, and (ii) a logistic growth model with state dependent carrying capacity, both of which…

## 4 Citations

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

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We investigate the most probable phase portrait (MPPP) of a stochastic single-species model with the Allee e ﬀ ect using the non-local Fokker-Planck equation. This stochastic model is driven by…

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A SIR coronavirus mathematical model is presented and it is considered that the contact rate is perturbed by Lévy noise, and the basic reproduction number that determines the extinction and the persistence of the disease (infection) is derived.

### Controlling mean exit time of stochastic dynamical systems based on quasipotential and machine learning

- Computer ScienceArXiv
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This work designs a systematic iterated numerical algorithm to calculate the controller for a given mean exit time of general stochastic dynamical systems and identifies the most probable path between metastable attractors with help of the Hamilton-Jacobi scheme and trained neural network.

### Slow manifolds for stochastic Koper models with stable L\'evy noises

- Mathematics
- 2022

The Koper model is a vector ﬁeld in which the di ﬀ erential equations describe the electrochemical oscillations appearing in di ﬀ usion processes. This work focuses on the understanding of the slow…

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