Editing Chaos theory (section)

===Other areas===
In chemistry, predicting gas solubility is essential to manufacturing [[polymers]], but models using [[particle swarm optimization]] (PSO) tend to converge to the wrong points. An improved version of PSO has been created by introducing chaos, which keeps the simulations from getting stuck.<ref>{{cite journal|last=Li|first=Mengshan|author2=Xingyuan Huanga|author3=Hesheng Liua|author4=Bingxiang Liub|author5=Yan Wub|author6=Aihua Xiongc|author7=Tianwen Dong|title=Prediction of gas solubility in polymers by back propagation artificial neural network based on self-adaptive particle swarm optimization algorithm and chaos theory|journal=Fluid Phase Equilibria|date=25 October 2013|volume=356|pages=11–17|doi=10.1016/j.fluid.2013.07.017|bibcode=2013FlPEq.356...11L }}</ref> In [[celestial mechanics]], especially when observing asteroids, applying chaos theory leads to better predictions about when these objects will approach Earth and other planets.<ref>{{cite journal|last=Morbidelli|first=A.|title=Chaotic diffusion in celestial mechanics|journal=Regular & Chaotic Dynamics |year=2001|volume=6|issue=4|pages=339–353|doi=10.1070/rd2001v006n04abeh000182}}</ref> Four of the five [[moons of Pluto]] rotate chaotically. In [[quantum physics]] and [[electrical engineering]], the study of large arrays of [[Josephson junctions]] benefitted greatly from chaos theory.<ref>Steven Strogatz, ''Sync: The Emerging Science of Spontaneous Order'', Hyperion, 2003</ref> Closer to home, coal mines have always been dangerous places where frequent natural gas leaks cause many deaths. Until recently, there was no reliable way to predict when they would occur. But these gas leaks have chaotic tendencies that, when properly modeled, can be predicted fairly accurately.<ref>{{cite journal|last=Dingqi|first=Li|author2=Yuanping Chenga|author3=Lei Wanga|author4=Haifeng Wanga|author5=Liang Wanga|author6=Hongxing Zhou|title=Prediction method for risks of coal and gas outbursts based on spatial chaos theory using gas desorption index of drill cuttings|journal=Mining Science and Technology|date=May 2011|volume=21|issue=3|pages=439–443|doi=10.1016/j.mstc.2011.05.010 |bibcode=2011MiSTC..21..439L }}</ref>

Chaos theory can be applied outside of the natural sciences, but historically nearly all such studies have suffered from lack of reproducibility; poor external validity; and/or inattention to cross-validation, resulting in poor predictive accuracy (if out-of-sample prediction has even been attempted). Glass<ref>{{cite book | last1 = Glass | first1 = L |editor1-first=C |editor1-last= Grebogi |editor2-first=J. A. | editor2-last=Yorke |title= The impact of chaos on science and society|publisher= United Nations University Press |year=1997 |chapter= Dynamical disease: The impact of nonlinear dynamics and chaos on cardiology and medicine }}</ref> and Mandell and Selz<ref>{{cite book | last1 = Mandell |first1= A. J. | last2 = Selz |first2= K. A. |editor1-first=C |editor1-last= Grebogi |editor2-first=J. A. | editor2-last=Yorke |title= The impact of chaos on science and society|publisher= United Nations University Press |year=1997 |chapter= Is the EEG a strange attractor? }}</ref> have found that no EEG study has as yet indicated the presence of strange attractors or other signs of chaotic behavior.

Redington and Reidbord (1992) attempted to demonstrate that the human heart could display chaotic traits. They monitored the changes in between-heartbeat intervals for a single psychotherapy patient as she moved through periods of varying emotional intensity during a therapy session. Results were admittedly inconclusive. Not only were there ambiguities in the various plots the authors produced to purportedly show evidence of chaotic dynamics (spectral analysis, phase trajectory, and autocorrelation plots), but also when they attempted to compute a Lyapunov exponent as more definitive confirmation of chaotic behavior, the authors found they could not reliably do so.<ref>{{cite journal|last1=Redington|first1=D. J.|last2=Reidbord|first2=S. P.|s2cid=214722|title=Chaotic dynamics in autonomic nervous system activity of a patient during a psychotherapy session|journal=Biological Psychiatry|date=1992|volume=31|issue=10|pages=993–1007|pmid=1511082|doi=10.1016/0006-3223(92)90093-F}}</ref>

In their 1995 paper, Metcalf and Allen<ref>{{cite book | last1 = Metcalf |first1= B. R. | last2 = Allen |first2= J. D. |editor1-first=F. D. |editor1-last= Abraham |editor2-first=A. R. | editor2-last=Gilgen |title= Chaos theory in psychology |publisher= Greenwood Press |year=1995 |chapter= In search of chaos in schedule-induced polydipsia }}</ref> maintained that they uncovered in animal behavior a pattern of period doubling leading to chaos. The authors examined a well-known response called schedule-induced polydipsia, by which an animal deprived of food for certain lengths of time will drink unusual amounts of water when the food is at last presented. The control parameter (r) operating here was the length of the interval between feedings, once resumed. The authors were careful to test a large number of animals and to include many replications, and they designed their experiment so as to rule out the likelihood that changes in response patterns were caused by different starting places for r.

Time series and first delay plots provide the best support for the claims made, showing a fairly clear march from periodicity to irregularity as the feeding times were increased. The various phase trajectory plots and spectral analyses, on the other hand, do not match up well enough with the other graphs or with the overall theory to lead inexorably to a chaotic diagnosis. For example, the phase trajectories do not show a definite progression towards greater and greater complexity (and away from periodicity); the process seems quite muddied. Also, where Metcalf and Allen saw periods of two and six in their spectral plots, there is room for alternative interpretations. All of this ambiguity necessitate some serpentine, post-hoc explanation to show that results fit a chaotic model.

By adapting a model of career counseling to include a chaotic interpretation of the relationship between employees and the job market, Amundson and Bright found that better suggestions can be made to people struggling with career decisions.<ref>{{cite journal|last=Pryor|first=Robert G. L.|author2=Norman E. Amundson|author3=Jim E. H. Bright|title=Probabilities and Possibilities: The Strategic Counseling Implications of the Chaos Theory of Careers|author3-link=Jim Bright (psychologist)|journal=The Career Development Quarterly|date=June 2008|volume=56|issue=4|pages=309–318|doi=10.1002/j.2161-0045.2008.tb00096.x}}</ref> Modern organizations are increasingly seen as open [[complex adaptive system]]s with fundamental natural nonlinear structures, subject to internal and external forces that may contribute chaos. For instance, [[team building]] and [[group development]] is increasingly being researched as an inherently unpredictable system, as the uncertainty of different individuals meeting for the first time makes the trajectory of the team unknowable.<ref>{{Cite journal|last1=Thompson|first1=Jamie|last2=Johnstone|first2=James|last3=Banks|first3=Curt|date=2018|title=An examination of initiation rituals in a UK sporting institution and the impact on group development|journal=European Sport Management Quarterly|volume=18|issue=5|pages=544–562|doi=10.1080/16184742.2018.1439984|s2cid=149352680}}</ref>

[[File:BML N=200 P=32.png|400px|right|The red cars and blue cars take turns to move; the red ones only move upwards, and the blue ones move rightwards. Every time, all the cars of the same colour try to move one step if there is no car in front of it. Here, the model has self-organized in a somewhat geometric pattern where there are some traffic jams and some areas where cars can move at top speed.]]

Traffic forecasting may benefit from applications of chaos theory. Better predictions of when a congestion will occur would allow measures to be taken to disperse it before it would have occurred. Combining chaos theory principles with a few other methods has led to a more accurate short-term prediction model (see the plot of the [[BML traffic model]] at right).<ref>{{cite journal|last=Wang|first=Jin|author2=Qixin Shi|title=Short-term traffic speed forecasting hybrid model based on Chaos–Wavelet Analysis-Support Vector Machine theory|journal=Transportation Research Part C: Emerging Technologies|date=February 2013|volume=27|pages=219–232|doi=10.1016/j.trc.2012.08.004|bibcode=2013TRPC...27..219W }}</ref>

Chaos theory has been applied to environmental [[water cycle]] data (also [[hydrological]] data), such as rainfall and streamflow.<ref>{{Cite web|url=http://pasternack.ucdavis.edu/research/projects/chaos-hydrology/|title=Dr. Gregory B. Pasternack – Watershed Hydrology, Geomorphology, and Ecohydraulics :: Chaos in Hydrology|website=pasternack.ucdavis.edu|language=en|access-date=2017-06-12}}</ref> These studies have yielded controversial results, because the methods for detecting a chaotic signature are often relatively subjective. Early studies tended to "succeed" in finding chaos, whereas subsequent studies and meta-analyses called those studies into question and provided explanations for why these datasets are not likely to have low-dimension chaotic dynamics.<ref>{{Cite journal|last=Pasternack|first=Gregory B.|date=1999-11-01|title=Does the river run wild? Assessing chaos in hydrological systems|journal=Advances in Water Resources|volume=23|issue=3|pages=253–260|doi=10.1016/s0309-1708(99)00008-1|bibcode = 1999AdWR...23..253P }}</ref>