Using the Logistic Map as Compared to the Cubic Map to Show the Convergence and the Relaxation of the Period–1 Fixed Point

Patrick Akwasi Anamuah Mensah, William Obeng-Denteh, Ibrahim Issaka, Kwasi Baah Gyamfi, Joshua Kiddy K. Asamoah and Harvinder S. Sidhu

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-7

Abstract: In this paper, we employ the logistic map and the cubic map to locate the relaxation and the convergence to the periodic fixed point of a system, specifically, the period—1 fixed point. The study has shown that the period—1 fixed point of a logistic map as a recurrence has its convergence at a transcritical bifurcation having its power-law fit with exponent β=−1 when α=1 and μ=0. The cubic map shows its convergence to the fixed point at a pitchfork bifurcation decaying at a power law with exponent β=−1/2α=1 and μ=0. However, the system shows their relaxation time at the same power law with exponents and z=−1.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:1255614

DOI: 10.1155/2022/1255614

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