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

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 trans...

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Bibliographic Details
Published in:International journal of mathematics and mathematical sciences 2022-07, Vol.2022, p.1-7
Main Authors: Akwasi Anamuah Mensah, Patrick, Obeng-Denteh, William, Issaka, Ibrahim, Baah Gyamfi, Kwasi, Asamoah, Joshua Kiddy K.
Format: Article
Language:English
Subjects:
Bifurcations
Comparative analysis
Convergence
Convergence (Social sciences)
Dynamical systems
Equilibrium
Laws, regulations and rules
Neighborhoods
Orbits
Power law
Relaxation time
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Summary: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.
ISSN:0161-1712
1687-0425
DOI:10.1155/2022/1255614