高斯色噪声激励下种群的动力学行为研究
Study on Dynamic Behavior of Population Excited by Gaussian Color Noise
摘要: 种群资源的开发利用是学术界的一个经典问题，对于此问题的研究，人类不光要考虑短期的经济效益，更应该注重生物资源的开发与可持续利用。而对于生物进化来说，种群为基本单位，是生态系统中不可分割的重要一部分，种群的生长情况是一项反应种群生态平衡的重要指标。通过引入经典的种群模型，研究在色噪声诱导下种群的动力学行为，对充分开发利用和保护种群资源有着举足轻重的意义。本文研究了在高斯色噪声作用下一种单种群系统的随机动力学行为。首先，通过统一有色噪声近似(UCNA)得到了Fokker-Planck方程，并进一步得到了种群的稳态密度函数以及平均首次穿越时间。然后，我们模拟和讨论了不同变量对平稳概率分布(SPD)和首次穿越时间的影响。并得到了乘性噪声强度和种群增长率的共振激活现象。
Abstract: The exploitation and utilization of population resources is a classic problem in academic circles. For the study of this problem, human beings should not only consider the short-term economic benefits, but also pay attention to the exploitation and sustainable utilization of biological resources. As for biological evolution, population is the basic unit and an important part of the ecosystem. The growth of population is an important index reflecting the ecological balance of population. By in-troducing the classical population model, the dynamic behavior of population induced by color noise is studied, which is of great significance to fully exploit and protect population resources. In this paper, the stochastic dynamic behavior of a single population system subjected to Gaussian color noise is studied. Firstly, the Fokker-Planck equation is obtained through the unified colored noise approximation (UCNA), and the steady-state density function and the mean first crossing time of the population are further obtained. Then, we simulate and discuss the effects of different varia-bles on stationary probability distribution (SPD) and first crossing time. The resonance activation phenomena of multiplicative noise intensity and population growth rate are obtained.
文章引用：冯雨顺, 李东喜. 高斯色噪声激励下种群的动力学行为研究[J]. 应用数学进展, 2022, 11(6): 3372-3384. https://doi.org/10.12677/AAM.2022.116360

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