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Critical junctures in the life of a chaotic attractor

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This article uses the logistic map as an example to illustrate the vagaries that afflict a chaotic attractor in the course of its progress along a path of varying parameter. Several critical junctures, called crises, are encountered, where the chaotic attractor either goes boom or bust!

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Suggested Reading

  1. J P Crutchfield, J D Fanner, N H Packard and R S Shaw, Chaos,Scientific American, Vol. 254, 46, 1986.

    Article  Google Scholar 

  2. R H Abraham and C D Shaw, Dynamics: The geometry of behavior. Part 2.Chaotic behavior, Aerial Press, Santa Cruz, CA, 1983.

    Google Scholar 

  3. P Cvitanovic,Universality in Chaos, Adam Hilger, Bristol, New York, 1989.

    Google Scholar 

  4. J Gleick,Chaos: Making of a New Science, Viking, New York, 1987

    Google Scholar 

  5. C Grebogi, E Ott and J A Yorke, Crises, sudden changes in chaotic attractors and transient chaos,Physica D, 7, 181, 1983

    Article  Google Scholar 

  6. B-L Hao,Chaos II, World Scientific, Singapore, 1990.

    Google Scholar 

  7. R V Jensen,Classical chaos,American Scientist,Vol. 75,1987.

  8. K Krishan, Manu and R Ramaswamy, Chaos, Resonance, Vol. 3, Nos. 4, 6, 10, 1998.

  9. R May,Simple mathematical models with very complicated dynamics, Sature, Vol. 261, 459, 1976.

    Google Scholar 

  10. S Strogatz,Nonlinear Dynamics and Chaos, Addison Wesley, Reading, Mass, 1994.

    Google Scholar 

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Correspondence to N. Ananthkrishnan or Tuhin Sahai.

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Ananthkrishnan, N., Sahai, T. Crises. Reson 6, 19–33 (2001).

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