Cobweb Diagram for Generalized Logistic Maps with z-Unimodality

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This Demonstration shows the cobweb diagram for , which generalizes the well-known logistic map [1–8]. Here is the iteration number, is the iterate of starting from the initial value , is the main control parameter, and is the subcontrol parameter (which determines the unimodality, the degree of the local maximum of ).

Contributed by: Ki-Jung Moon (December 2013)
Open content licensed under CC BY-NC-SA


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References

[1] R. L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed., Boulder: Westview Press, 2003.

[2] K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems, New York: Springer-Verlag, 1997.

[3] S. H. Strogatz, Nonlinear Dynamics and Chaos, Reading, MA: Perseus Books Publishing, 1994.

[4] S. Wolfram, A New Kind of Science, Champaign, IL: Wolfram Media, Inc., 2002.

[5] M. J. Feigenbaum, "Quantitative Universality for a Class of Nonlinear Transformations," Journal of Statistical Physics, 19(1), 1978 pp. 25–52. doi:10.1007/BF01020332.

[6] M. J. Feigenbaum, "The Universal Metric Properties of Nonlinear Transformations," Journal of Statistical Physics, 21(6), 1979 pp. 669–706. doi:10.1007/BF01107909.

[7] K.-J. Moon and S. D. Choi, "Reducible Expansions and Related Sharp Crossovers in Feigenbaum's Renormalization Field," Chaos: An Interdisciplinary Journal of Nonlinear Science, 18(2), 2008, 023104. doi:10.1063/1.2902826.

[8] K.-J. Moon, "Erratum: Reducible Expansions and Related Sharp Crossovers in Feigenbaum's Renormalization Field," Chaos: An Interdisciplinary Journal of Nonlinear Science, 20, 2010, 049902. doi:10.1063/1.3530128.



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