Editing Butterfly effect (section)

==== Differentiating types of butterfly effects ====
The concept of the butterfly effect encompasses several phenomena. The two kinds of butterfly effects, including the sensitive dependence on initial conditions,<ref name=":0" /> and the ability of a tiny perturbation to create an organized circulation at large distances,<ref name=":1" /> are not exactly the same.<ref>{{cite journal |last=Shen |first=Bo-Wen |date=2014-05-01 |title=Nonlinear Feedback in a Five-Dimensional Lorenz Model |url=https://journals.ametsoc.org/view/journals/atsc/71/5/jas-d-13-0223.1.xml |journal=Journal of the Atmospheric Sciences |language=EN |volume=71 |issue=5 |pages=1701–1723 |doi=10.1175/JAS-D-13-0223.1 |bibcode=2014JAtS...71.1701S |s2cid=123683839 |issn=0022-4928}}</ref> In Palmer et al.,<ref name=":3" /> a new type of butterfly effect is introduced, highlighting the potential impact of small-scale processes on finite predictability within the Lorenz 1969 model. Additionally, the identification of ill-conditioned aspects of the Lorenz 1969 model points to a practical form of finite predictability.<ref name=":7" /> These two distinct mechanisms suggesting finite predictability in the Lorenz 1969 model are collectively referred to as the third kind of butterfly effect.<ref name=":8" /> The authors in <ref name=":8" /> have considered Palmer et al.'s suggestions and have aimed to present their perspective without raising specific contentions.

The third kind of butterfly effect with finite predictability, as discussed in,<ref name=":3" /> was primarily proposed based on a convergent geometric series, known as Lorenz's and Lilly's formulas. Ongoing discussions are addressing the validity of these two formulas for estimating predictability limits in.<ref>{{Cite journal |last1=Shen |first1=Bo-Wen |last2=Pielke Sr. |first2=Roger |last3=Zeng |first3=Xubin |date=2024-07-24 |title=Revisiting Lorenz's and Lilly's Empirical Formulas for Predictability Estimates |url=https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2228/ |journal=EGUsphere |language=English |pages=1–0 |doi=10.13140/RG.2.2.32941.15849}}</ref>

A comparison of the two kinds of butterfly effects<ref name=":1" /><ref name=":0" /> and the third kind of butterfly effect<ref name=":2" /><ref name=":3" /><ref name=":4" /> has been documented.<ref name=":8">{{cite journal |last1=Shen |first1=Bo-Wen |last2=Pielke |first2=Roger A. |last3=Zeng |first3=Xubin |last4=Cui |first4=Jialin |last5=Faghih-Naini |first5=Sara |last6=Paxson |first6=Wei |last7=Atlas |first7=Robert |date=2022-07-04 |title=Three Kinds of Butterfly Effects within Lorenz Models |journal=[[Encyclopedia (journal)|Encyclopedia]] |language=en |volume=2 |issue=3 |pages=1250–1259 |issn=2673-8392 |doi=10.3390/encyclopedia2030084 |doi-access=free}}</ref> In recent studies,<ref name=":7" /><ref>{{Cite journal |last1=Saiki |first1=Yoshitaka |last2=Yorke |first2=James A. |date=2023-05-02 |title=Can the Flap of a Butterfly's Wings Shift a Tornado into Texas&mdash;Without Chaos? |journal=Atmosphere |language=en |volume=14 |issue=5 |pages=821 |doi=10.3390/atmos14050821 |bibcode=2023Atmos..14..821S |issn=2073-4433 |doi-access=free }}</ref> it was reported that both meteorological and non-meteorological linear models have shown that instability plays a role in producing a butterfly effect, which is characterized by brief but significant exponential growth resulting from a small disturbance.