On the Convergence of Logistic Map in NOOR Orbit

Chugh, Renu; Rani, Mamta; Ashish, Ashish

doi:10.5120/6200-8739

Cited by 5 publications

(2 citation statements)

References 18 publications

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“…In 1953, Mann (1953 introduced a novel three-step feedback procedure also known as Mann iterative method which give superior results in functional analysis and every branch of mathematics. Further, Chugh et al (2012), in 2012 examined the stability and convergence of the logistic map using another four-step feedback procedure also known as Noor iterative method. and studied the dynamics of the generalized logistic map in superior orbit (see also Renu et al (2022)).…”

Section: Introductionmentioning

confidence: 99%

Dynamical Interpretation of Logistic Map using Euler’s Numerical Algorithm

Sanjeev¹,

Anjali

ASHİSH³

et al. 2022

Chaos Theory and Applications

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In the last two decades, the dynamics of difference and differential equations have found a celebrated place in science and engineering such as weather forecasting, secure communication, transportation problems, biology, the population of species, etc. In this article, we deal with the dynamical behavior of the logistic map using Euler’s numerical algorithm. The dynamical properties of Euler’s type logistic system are derived analytically as well as experimentally. In the analytical section, the dynamical properties such as fixed point, period-doubling, and irregularity are examined followed by s few theorems. Further, in the experimental section, the dynamical properties of Euler’s type logistic system are studied using period-doubling bifurcation plots. Because the dynamics of the Euler’s map depend on the Euler’s control parameter h, therefore, three major cases are discussed for all the dynamical properties for h = 0.1, 0.4, and 0.7.

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Section: Introductionmentioning

confidence: 99%

Dynamical Interpretation of Logistic Map using Euler’s Numerical Algorithm

Sanjeev¹,

Anjali

ASHİSH³

et al. 2022

Chaos Theory and Applications

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“…Nowadays, chaotic dynamical systems have been used for various purposes, for example, to modeling an image encryption in cryptography [12]- [14], to secure communication system and generate chaotic signals [15], to design noise generator system and QT circuit [16], [17] . Further, detailed scientific applications of logistic map have been presented by Peitgen et al [18], Chowdhary et al [19], Devaney [20], Chugh et al [21], Sharkovsky et al [22] etc.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of Logistic Map Using Four Step Feedback Procedure

Kumari¹,

Chugh²,

Nandal³

2019

IJEAT

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The logistic map occupies a renowned place in the dynamics of chaos theory and in diverse areas of science. Picard orbit and Superior orbit (Mann orbit) have been used to control this discrete chaotic dynamical system. In this article, we further extend the analytical study of logistic map using a four step feedback procedure (SP orbit). The dynamical properties such as fixed point, range of convergence and stability, periodicity and chaos of the logistic map have been investigated. These properties are illustrated experimentally by adopting dynamical techniques like fixed point analysis and bifurcation plot. Using this approach, one can easily control the chaotic system and make the system stable for higher values of population growth parameter r by selecting the control parameters carefully.

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A novel four-step feedback procedure for rapid control of chaotic behavior of the logistic map and unstable traffic on the road

Kumari

Chugh

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We present a new four-step feedback procedure to study the full dynamics of a nonlinear dynamical system, namely, the logistic map. We show that by using this procedure, the chaotic behavior of the logistic map can be controlled easily and rapidly or the system can be made stable for higher values of the population growth parameter. We utilize various dynamical techniques (orbit evolution, time series analysis, bifurcation diagrams, and Lyapunov exponents) to analyze the dynamics of the logistic map. Additionally, we adopt the switching strategy to control chaos or to increase the stability performance of the logistic map. Finally, we propose a modified traffic control model to enable rapid control of unexpected traffic on the road. The results of this model are supported by a physical interpretation. The model is found to be more efficient than existing models of Lo and Cho [J. Franklin Inst. 342, 839–851 (2005)] and Ashish et al. [Nonlinear Dyn. 94, 959–975 (2018)]. This work provides a novel feedback procedure that facilitates rapid control of chaotic behavior and increases the range of stability of dynamical systems.

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On the Convergence of Logistic Map in NOOR Orbit

Cited by 5 publications

References 18 publications

Dynamical Interpretation of Logistic Map using Euler’s Numerical Algorithm

Dynamical Interpretation of Logistic Map using Euler’s Numerical Algorithm

Bifurcation Analysis of Logistic Map Using Four Step Feedback Procedure

A novel four-step feedback procedure for rapid control of chaotic behavior of the logistic map and unstable traffic on the road

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