2022/07/04 by Bo‐Wen Shen, Roger A. Pielke, Xubin Zeng +4 · 1 citation
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation #Chaos control and synchronization
paper · pdf · doi:10.3390/encyclopedia2030084
openalex publication_date 2022/07/04 · openalex created_date 2022/07/05 · openalex updated_date 2026/08/01
Within Lorenz models, the three major kinds of butterfly effects (BEs) are the sensitive dependence on initial conditions (SDIC), the ability of a tiny perturbation to create an organized circulation at large distances, and the hypothetical role of small-scale processes in contributing to finite predictability, referred to as the first, second, and third kinds of butterfly effects (BE1, BE2, and BE3), respectively. A well-accepted definition of the butterfly effect is the BE1 with SDIC, which was rediscovered by Lorenz in 1963. In fact, the use of the term “butterfly” appeared in a conference presentation by Lorenz in 1972, when Lorenz introduced the BE2 as the metaphorical butterfly effect. In 2014, the so-called “real butterfly effect”, which is based on the features of Lorenz’s study in 1969, was introduced as the BE3.