关键词: 随机微分方程 , 环境噪声 , 群集效应

Abstract: The cluster effect is an evolution phenomenon that often appears in natural and social sciences. The in-depth study of this kind of phenomenon is expected to fundamentally solve the reliability problem of the relevant system, and thus has considerable application value. The purpose of this paper is to study the individual clustering problem driven by the environmental noise. By using ordinary differential equation and stochastic differential equation to model the phenomenon, analyze and compare the asymptotic behavior of the solution, we get an important conclusion: under the same assumptions, ordinary differential equations do not produce clustering effect, while stochastic differential equations produce clustering effect, that is, the environmental noise can promote the individual clustering phenomenon. Finally, by giving specific values to the model's parameters and aplotting a comparison diagram, it is intuitively shown that the environmental noise leads to individual cluster effect, which is consistent with our theoretical results.

Key words: Stochastic differential equation ,  , Environmental noise ,  , Flocking effect