Editing Chaos theory (section)

===Biology===
For over a hundred years, biologists have been keeping track of populations of different species with [[population model]]s. Most models are [[continuous function|continuous]], but recently scientists have been able to implement chaotic models in certain populations.<ref>{{cite journal|last=Eduardo|first=Liz|author2=Ruiz-Herrera, Alfonso|title=Chaos in discrete structured population models|journal=[[SIAM Journal on Applied Dynamical Systems]]|year=2012|volume=11|issue=4|pages=1200–1214|doi=10.1137/120868980}}</ref> For example, a study on models of [[Canada lynx|Canadian lynx]] showed there was chaotic behavior in the population growth.<ref>{{cite journal|last=Lai|first=Dejian|title=Comparison study of AR models on the Canadian lynx data: a close look at BDS statistic|journal=[[Computational Statistics & Data Analysis]]|year=1996|volume=22|issue=4|pages=409–423|doi=10.1016/0167-9473(95)00056-9}}</ref> Chaos can also be found in ecological systems, such as [[hydrology]]. While a chaotic model for hydrology has its shortcomings, there is still much to learn from looking at the data through the lens of chaos theory.<ref>{{cite journal|last=Sivakumar|first=B|title=Chaos theory in hydrology: important issues and interpretations|journal=[[Journal of Hydrology]]|date=31 January 2000|volume=227|issue=1–4|pages=1–20|bibcode=2000JHyd..227....1S|doi=10.1016/S0022-1694(99)00186-9}}</ref> Another biological application is found in [[cardiotocography]]. Fetal surveillance is a delicate balance of obtaining accurate information while being as noninvasive as possible. Better models of warning signs of [[Intrauterine hypoxia|fetal hypoxia]] can be obtained through chaotic modeling.<ref>{{cite journal|last=Bozóki|first=Zsolt|title=Chaos theory and power spectrum analysis in computerized cardiotocography|journal=[[European Journal of Obstetrics & Gynecology and Reproductive Biology]]|date=February 1997|volume=71|issue=2|pages=163–168|doi=10.1016/s0301-2115(96)02628-0|pmid=9138960}}</ref>

As Perry points out, [[mathematical model|modeling]] of chaotic [[time series]] in [[theoretical ecology|ecology]] is helped by constraint.<ref name=realdata/>{{rp|176,177}} There is always potential difficulty in distinguishing real chaos from chaos that is only in the model.<ref name=realdata/>{{rp|176,177}} Hence both constraint in the model and or duplicate time series data for comparison will be helpful in constraining the model to something close to the reality, for example Perry & Wall 1984.<ref name=realdata>{{cite book|year=2000|edition=1|publisher=[[Springer Science+Business Media Dordrecht]]|first4=David|first3=Ian|first2=Robert|first1=Joe|last4=Morse|last2=Smith|last1=Perry|last3=Woiwod|editor-first1=Joe N|editor-first2=Robert H|editor-first3=Ian P|editor-first4=David R|editor-last1=Perry|editor-last2=Smith|editor-last3=Woiwod|editor-last4=Morse|pages=xii+226|title=Chaos in Real Data : The Analysis of Non-Linear Dynamics from Short Ecological Time Series|series=[[Population and Community Biology Series]]|doi=10.1007/978-94-011-4010-2|isbn=978-94-010-5772-1|s2cid=37855255}}</ref>{{rp|176,177}} [[Gene-for-gene]] co-evolution sometimes shows chaotic dynamics in [[allele frequencies]].<ref name = "GFG" /> Adding variables exaggerates this: Chaos is more common in [[evolutionary model|models]] incorporating additional variables to reflect additional facets of real populations.<ref name = "GFG" /> [[Robert M. May]] himself did some of these foundational crop co-evolution studies, and this in turn helped shape the entire field.<ref name = "GFG" >
 {{ Cite journal |
       language=en|
           year=1992|
      publisher=[[Nature Publishing Group]]|
         volume=360|
        journal=[[Nature (journal)|Nature]]|
           issn=0028-0836|
          eissn=1476-4687|
         first2=Jeremy|
         first1=John|
     department=Review Article|
          pages=121–125|
          last1=Thompson|
          last2=Burdon|
          title=Gene-for-gene coevolution between plants and parasites|
 issue=6400|
            doi=10.1038/360121a0|
 bibcode=1992Natur.360..121T|
 s2cid=4346920}}
</ref> Even for a steady environment, merely combining one [[crop]] and one [[pathogen]] may result in [[quasiperiodicity|quasi-periodic-]] or [[chaotic oscillation|chaotic-]] oscillations in pathogen [[statistical population|population]].<ref name = "Epidemiology" >
 {{ Cite book |
       language=en|
           year=1998|
        edition=1|
      publisher=[[Springer Science+Business Media Dordrecht]]|
          first=Gareth|
           last=Jones|
 editor-first1=D. Gareth|
 editor-last1=Jones|
          pages=xvi + 460 + 26{{NBSP}}b/w{{NBSP}}{{NBSP}}ill. + 33{{NBSP}}color{{NBSP}}ill|
          title=The Epidemiology of Plant Diseases|
            doi=10.1007/978-94-017-3302-1|
          s2cid=1793087|
           isbn=978-94-017-3302-1}}
</ref>{{ RP |page=169}}