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该映射可作为离散激光的动力学模型，其中，<math>x</math>可以代表电场振幅，<math>G</math>为为激光增益分岔参数。
该映射可作为离散激光的动力学模型，其中，<math>x</math>可以代表电场振幅，<math>G</math>为为激光增益分岔参数。<ref name="Okulov, A Yu 1986">{{cite journal|last1=Okulov|first1=A Yu|last2=Oraevskiĭ|first2=A N|year=1986|title=Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium|journal=J. Opt. Soc. Am. B|volume=3|issue=5|pages=741–746|bibcode=1986OSAJB...3..741O|doi=10.1364/JOSAB.3.000741}}</ref>
容易观察到，该映射其具有与Logistic映射类似的性质，当<math>G</math>在区间<math>[0，\infty) </math>中逐渐增大时，其动力学由规则型变为混沌型，<ref name="Okulov, A Yu 1984">{{cite journal|last1=Okulov|first1=A Yu|last2=Oraevskiĭ|first2=A N|year=1984|title=Regular and stochastic self-modulation in a ring laser with nonlinear element|journal=Soviet Journal of Quantum Electronics|volume=14|issue=2|pages=1235–1237|bibcode=1984QuEle..14.1235O|doi=10.1070/QE1984v014n09ABEH006171}}</ref> 其分岔图在某些性质上与Logistic映射相同。
容易观察到，该映射其具有与Logistic映射类似的性质，当<math>G</math>在区间<math>[0，\infty) </math>中逐渐增大时，其动力学由规则型变为混沌型，<ref name="Okulov, A Yu 1984">{{cite journal|last1=Okulov|first1=A Yu|last2=Oraevskiĭ|first2=A N|year=1984|title=Regular and stochastic self-modulation in a ring laser with nonlinear element|journal=Soviet Journal of Quantum Electronics|volume=14|issue=2|pages=1235–1237|bibcode=1984QuEle..14.1235O|doi=10.1070/QE1984v014n09ABEH006171}}</ref> 其分岔图在某些性质上与Logistic映射相同。
除此之外，该映射也有相同的费根鲍姆常数（包括<math>\delta</math>=4.669201...,<math>\alpha</math>=2.502907...）<ref>[http://chaosbook.org/extras/mjf/LA-6816-PR.pdf Feigenbaum, M. J. (1976) "Universality in complex discrete dynamics", Los Alamos Theoretical Division Annual Report 1975-1976]</ref>。<ref name="Okulov, A Yu 1986">{{cite journal|last1=Okulov|first1=A Yu|last2=Oraevskiĭ|first2=A N|year=1986|title=Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium|journal=J. Opt. Soc. Am. B|volume=3|issue=5|pages=741–746|bibcode=1986OSAJB...3..741O|doi=10.1364/JOSAB.3.000741}}</ref>。
除此之外，该映射也有相同的费根鲍姆常数（包括<math>\delta</math>=4.669201...,<math>\alpha</math>=2.502907...）<ref>[http://chaosbook.org/extras/mjf/LA-6816-PR.pdf Feigenbaum, M. J. (1976) "Universality in complex discrete dynamics", Los Alamos Theoretical Division Annual Report 1975-1976]</ref>。。
由此，可见费根鲍姆常数具有很强的普适性。
由此，可见费根鲍姆常数具有很强的普适性。