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Phenomenological bifurcation in a generally stochastic population model with Allee effect
1Finance Depatment, Jiangsu University, Zhenjiang, 212013, Jiangsu, China. wanghc1101@sina.com.
The European Physical Journal. E, Soft Matter
|October 29, 2022
Summary
Correlated noises can induce bifurcations in population models with Allee effects. The intensity of these noises influences the population
Area of Science:
- Mathematical Biology
- Stochastic Processes
- Ecology
Background:
- Population dynamics are often influenced by environmental stochasticity.
- The Allee effect describes reduced per capita growth at low population densities.
- Understanding noise impacts is crucial for realistic ecological modeling.
Purpose of the Study:
- Investigate noise-induced phenomenological bifurcation (P-bifurcation) in a population model with Allee effect.
- Analyze the influence of correlated additive and multiplicative white noises on population dynamics.
- Examine how noise intensity affects the stationary probability distribution (SPD).
Main Methods:
- Utilized the Fokker-Planck equation to derive the stationary probability distribution (SPD).
- Performed detailed analysis and simulations on stochastic logistic-like models.
- Considered both weak and strong Allee effects under correlated noise conditions.
Main Results:
- Identified a critical noise intensity value at which the SPD shape transitions, indicating P-bifurcation.
- Demonstrated that correlated noises significantly alter the eventual distribution of population size.
- Observed complex effects of correlated noises on population dynamics.
Conclusions:
- Noise-induced P-bifurcation is a key phenomenon in population models with Allee effects.
- Correlated additive and multiplicative noises play a complex role in shaping population distributions.
- The findings highlight the importance of considering stochasticity in ecological modeling.
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