A chaotic map with infinite number of equilibria in a bounded domain

Wang, Zhen; Khalaf, Abdul Jalil M.; Tian, Huaigu; Alsaedi, Ahmed; Hayat, Tasawar

doi:10.1140/epjst/e2020-900172-0

Cited by 7 publications

(3 citation statements)

References 51 publications

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“…Let us consider the following one dimensional map, which has been recently proposed in [49] as an example of an elegant map that can display chaotic behavior:…”

Section: The New Fractional Mapmentioning

confidence: 99%

A New Fractional‐Order Map with Infinite Number of Equilibria and Its Encryption Application

et al. 2022

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The study of the chaotic dynamics in fractional-order discrete-time systems has received great attention over the last years. Some efforts have been also devoted to analyze fractional maps with special features. This paper makes a contribution to the topic by introducing a new fractional map that is characterized by both particular dynamic behaviors and specific properties related to the system equilibria. In particular, the conceived one dimensional map is algebraically simpler than all the proposed fractional maps in the literature. Using numerical simulation, we investigate the dynamic and complexity of the fractional map. The results indicate that the new one-dimensional fractional map displays various types of coexisting attractors. The approximate entropy is used to observe the changes in the sequence sequence complexity when the fractional order and system parameter. Finally, the fractional map is applied to the problem of encrypting electrophysiological signals. For the encryption process, random numbers were generated using the values of the fractional map. Some statistical tests are given to show the performance of the encryption.

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“…Let us consider the following one dimensional map, which has been recently proposed in [49] as an example of an elegant map that can display chaotic behavior:…”

Section: The New Fractional Mapmentioning

confidence: 99%

A New Fractional‐Order Map with Infinite Number of Equilibria and Its Encryption Application

et al. 2022

View full text Add to dashboard Cite

show abstract

“…While most papers in this special issue are about chaotic flows, some works about chaotic maps are presented [57][58][59][60]. In [58], the authors study relatively simple examples of non-autonomous maps having different changes in time chaotic attractors.…”

mentioning

confidence: 99%

“…The results of the numerical simulation show that the variation process of the parameters can positively affect the sensitivity of the system to its initial conditions, which increase the values of the largest Lyapunov exponent. In [60], the authors introduce a dynamical map with an infinite number of equilibrium points. Although chaotic flows with special properties in their equilibria have been investigated widely, this kind of work on chaotic maps has been neglected.…”

mentioning

confidence: 99%