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… 

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

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

Stochastic COVID-19 Model Influenced by Non-Gaussian Noise (preprint)/ en

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

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

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

References

SHOWING 1-10 OF 59 REFERENCES

Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

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.

Stochastic bifurcations in a bistable Duffing-Van der Pol oscillator with colored noise.

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.

Stochastic bifurcation for two-time-scale dynamical system with α-stable Lévy noise

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

Mean exit time and escape probability for the stochastic logistic growth model with multiplicative α-stable Lévy noise

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

Elementary bifurcations for a simple dynamical system under non-Gaussian Lévy noises

A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits

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.

Logistic equation is a simple stochastic carrying capacity

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.
...