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Phenomenological bifurcation in a generally stochastic population model with Allee effect

  • Regular Article - Living Systems
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Abstract

A general population model with Allee effect driven by correlated additive and multiplicative white noises is considered. This paper aims to investigate noise-induced phenomenological bifurcation (P-bifurcation) and the influence of noises on the population model. With the help of Fokker–Planck equation, we obtain the stationary probability distribution (SPD) of the model, and find that the shape of SPD experiences a transition from one structure to another when the noise intensity passes through a critical value, i.e., the P-bifurcation occurs. Moreover, detailed analysis and simulations for stochastic logistic-like models with weak and strong Allee effects show that the correlated noises have complex effects on the eventual distribution of population size.

Graphical abstract

This paper aims to investigate noise-induced phenomenological bifurcation (P-bifurcation) for a general population model with Allee effect driven by correlated additive and multiplicative white noises. We find that the shape of SPD experiences a transition from one structure to another when the noise intensity passes through a critical value, i.e., the P-bifurcation occurs.

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Acknowledgements

This work was jointly supported by the grants from National Natural Science Foundation of China (12161005, 62173161, 11801224) and Natural Science Foundation of Jiangsu Province (BK20180856).

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  1. Finance Depatment, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Hongcui Wang

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  1. Hongcui Wang
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Correspondence to Hongcui Wang.

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Wang, H. Phenomenological bifurcation in a generally stochastic population model with Allee effect. Eur. Phys. J. E 45, 87 (2022). https://doi.org/10.1140/epje/s10189-022-00235-w

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