Detecting Transitions from Steady States to Chaos with Gamma Distribution

作者：Haiyan Wang, Ying Wang · 发表于：International Journal of Bifurcation and Chaos · 年份：2025 · DOI：10.1142/s0218127425501639 · 被引用次数：2 · 研究领域：Complex Systems and Time Series Analysis

In this paper, we introduce a novel method to identify transitions from steady states to chaos in stochastic models, specifically focusing on the logistic and Ricker equations by leveraging the gamma distribution to describe the underlying population. We begin by showing that when the variance is sufficiently small, the stochastic equations converge to their deterministic counterparts. Our analysis reveals that the stochastic equations exhibit two distinct branches of the intrinsic growth rate, corresponding to alternative stable states characterized by higher and lower growth rates. Notably, while the logistic model does not show a transition from a steady-state to chaos, the Ricker model undergoes such a transition when the shape parameter of the gamma distribution is small. These findings not only enhance our understanding of the dynamic behavior in biological populations but also provide a robust framework for detecting chaos in complex systems.