Editing Butterfly effect (section)

==== Revised perspectives on chaotic and non-chaotic systems ====
By revealing coexisting chaotic and non-chaotic attractors within Lorenz models, Shen and his colleagues proposed a revised view that "weather possesses chaos and order", in contrast to the conventional view of "weather is chaotic".<ref>{{cite journal |last1=Shen |first1=Bo-Wen |last2=Pielke |first2=Roger A. |last3=Zeng |first3=Xubin |last4=Baik |first4=Jong-Jin |last5=Faghih-Naini |first5=Sara |last6=Cui |first6=Jialin |last7=Atlas |first7=Robert |date=2021-01-01 |title=Is Weather Chaotic?: Coexistence of Chaos and Order within a Generalized Lorenz Model |journal=Bulletin of the American Meteorological Society |language=EN |volume=102 |issue=1 |pages=E148–E158 |doi=10.1175/BAMS-D-19-0165.1 |bibcode=2021BAMS..102E.148S |s2cid=208369617 |issn=0003-0007 |doi-access=free}}</ref><ref>{{cite book |last1=Shen |first1=Bo-Wen |last2=Pielke |first2=R. A. Sr. |last3=Zeng |first3=X. |last4=Baik |first4=J.-J. |last5=Faghih-Naini |first5=S. |last6=Cui |first6=J. |last7=Atlas |first7=R. |last8=Reyes |first8=T. A. L. |title=13th Chaotic Modeling and Simulation International Conference |chapter=Is Weather Chaotic? Coexisting Chaotic and Non-chaotic Attractors within Lorenz Models |date=2021 |editor-last=Skiadas |editor-first=Christos H. |editor2-last=Dimotikalis |editor2-first=Yiannis |chapter-url=https://link.springer.com/chapter/10.1007/978-3-030-70795-8_57 |series=Springer Proceedings in Complexity |language=en |location=Cham |publisher=Springer International Publishing |pages=805–825 |doi=10.1007/978-3-030-70795-8_57 |isbn=978-3-030-70795-8 |s2cid=245197840}}</ref><ref>{{cite journal |last=Anthes |first=Richard A. |date=2022-08-14 |title=Predictability and Predictions |journal=Atmosphere |language=en |volume=13 |issue=8 |pages=1292 |doi=10.3390/atmos13081292 |bibcode=2022Atmos..13.1292A |issn=2073-4433 |doi-access=free}}</ref> As a result, sensitive dependence on initial conditions (SDIC) does not always appear. Namely, SDIC appears when two orbits (i.e., solutions) become the chaotic attractor; it does not appear when two orbits move toward the same point attractor. The above animation for [[double pendulum]] motion provides an analogy. For large angles of swing the motion of the pendulum is often chaotic.<ref>{{citation |last1=Richter |first1=P. H. |title=Chaos in Classical Mechanics: The Double Pendulum |last2=Scholz |first2=H.-J. |date=1984 |work=Stochastic Phenomena and Chaotic Behaviour in Complex Systems |series=Springer Series in Synergetics |volume=21 |pages=86–97 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |isbn=978-3-642-69593-3 |doi=10.1007/978-3-642-69591-9_9 |url=https://link.springer.com/chapter/10.1007/978-3-642-69591-9_9 |access-date=2022-07-11}}</ref><ref>{{cite journal |last=Shinbrot |first=Troy, Celso A Grebogi, Jack Wisdom, James A Yorke |date=1992 |title=Chaos in a double pendulum |url=https://doi.org/10.1119/1.16860 |journal=American Journal of Physics |volume=60 |issue=6 |pages=491–499 |doi=10.1119/1.16860 |bibcode=1992AmJPh..60..491S}}</ref> By comparison, for small angles of swing, motions are non-chaotic.
Multistability is defined when a system (e.g., the [[double pendulum]] system) contains more than one bounded attractor that depends only on initial conditions. The multistability was illustrated using kayaking in Figure on the right side (i.e., Figure 1 of <ref name=":6">{{cite journal |last1=Shen |first1=Bo-Wen |last2=Pielke Sr. |first2=Roger Pielke |last3=Zeng |first3=Xubin |last4=Cui |first4=Jialin |last5=Faghih-Naini |first5=Sara |last6=Paxson |first6=Wei |last7=Kesarkar |first7=Amit |last8=Zeng |first8=Xiping |last9=Atlas |first9=Robert |date=2022-11-12 |title=The Dual Nature of Chaos and Order in the Atmosphere |journal=Atmosphere |language=en |volume=13 |issue=11 |pages=1892 |doi=10.3390/atmos13111892 |bibcode=2022Atmos..13.1892S |issn=2073-4433 |doi-access=free}} [[File:CC-BY icon.svg|50px]] Text was copied from this source, which is available under a [https://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International License].</ref>) where the appearance of strong currents and a stagnant area suggests instability and local stability, respectively. As a result, when two kayaks move along strong currents, their paths display SDIC. On the other hand, when two kayaks move into a stagnant area, they become trapped, showing no typical SDIC (although a chaotic transient may occur). Such features of SDIC or no SDIC suggest two types of solutions and illustrate the nature of multistability.

By taking into consideration time-varying multistability that is associated with the modulation of large-scale processes (e.g., seasonal forcing) and aggregated feedback of small-scale processes (e.g., convection), the above revised view is refined as follows:

"The atmosphere possesses chaos and order; it includes, as examples, emerging organized systems (such as tornadoes) and time varying forcing from recurrent seasons."<ref name=":6"/><ref>{{cite web |last=Shen |first=Bo-Wen |date=21 Feb 2023 |title=Exploring Chaos Theory for Monstability and Multistability |website=[[YouTube]] |url=https://www.youtube.com/watch?v=GXtpkf3QsPI}}</ref>