# 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}
}
• Published 13 October 2020
• Mathematics
• Journal of Statistical Mechanics: Theory and Experiment
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…
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## References

SHOWING 1-10 OF 59 REFERENCES

• Mathematics
• 2021
It is observed that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., the stochastic model is more realistic than the deterministic one, and this phenomenon is illustrated with some numerical simulations.
• Engineering
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2011
Gaussian colored-noise-induced stochastic bifurcations and the dynamical influence of correlation time and noise intensity in a bistable Duffing-Van der Pol oscillator are investigated and the effects of multiplicative noise are rather different from that of additive noise.
• Mathematics
• 2021
This work focuses on stochastic bifurcation for a slow–fast dynamical system driven by non-Gaussian α-stable Lévy noise. We prove the main result for the stochastic equilibrium states for the
• Mathematics
• 2020
In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure
• Mathematics
Int. J. Bifurc. Chaos
• 2018
Stochastic bifurcation for a system under multiplicative stable Levy noise is studied by examining the qualitative changes of equilibrium states in its most probable phase portraits, and finds some peculiar bIfurcation phenomena in contrast to the deterministic counterpart.
• Biology
• 2016
The logistic model has long been used in ecological modelling for its simplicity and effectiveness but, to date, there are a limited number of models that incorporate the stochastic nature of the carrying capacity.