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Entropy 2013, 15(10), 4310-4318; doi:10.3390/e15104310
Article

Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation

1,2,* , 1
 and 1,3
Received: 14 August 2013; in revised form: 25 September 2013 / Accepted: 1 October 2013 / Published: 14 October 2013
(This article belongs to the Special Issue Dynamical Systems)
Download PDF [133 KB, uploaded 14 October 2013]
Abstract: Convergence to a period one fixed point is investigated for both logistic and cubic maps. For the logistic map the relaxation to the fixed point is considered near a transcritical bifurcation while for the cubic map it is near a pitchfork bifurcation. We confirmed that the convergence to the fixed point in both logistic and cubic maps for a region close to the fixed point goes exponentially fast to the fixed point and with a relaxation time described by a power law of exponent -1. At the bifurcation point, the exponent is not universal and depends on the type of the bifurcation as well as on the nonlinearity of the map.
Keywords: relaxation to fixed points; dissipative mapping; complex system; cubic map; logistic map relaxation to fixed points; dissipative mapping; complex system; cubic map; logistic map
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

de Oliveira, J.A.; Papesso, E.R.; Leonel, E.D. Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation. Entropy 2013, 15, 4310-4318.

AMA Style

de Oliveira JA, Papesso ER, Leonel ED. Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation. Entropy. 2013; 15(10):4310-4318.

Chicago/Turabian Style

de Oliveira, Juliano A.; Papesso, Edson R.; Leonel, Edson D. 2013. "Relaxation to Fixed Points in the Logistic and Cubic Maps: Analytical and Numerical Investigation." Entropy 15, no. 10: 4310-4318.


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