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Fractional Form of a Chaotic Map without Fixed Points: Chaos, Entropy and Control

In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase...

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Detalles Bibliográficos
Autores principales: Ouannas, Adel, Wang, Xiong, Khennaoui, Amina-Aicha, Bendoukha, Samir, Pham, Viet-Thanh, Alsaadi, Fawaz E.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512281/
https://www.ncbi.nlm.nih.gov/pubmed/33265809
http://dx.doi.org/10.3390/e20100720
Descripción
Sumario:In this paper, we investigate the dynamics of a fractional order chaotic map corresponding to a recently developed standard map that exhibits a chaotic behavior with no fixed point. This is the first study to explore a fractional chaotic map without a fixed point. In our investigation, we use phase plots and bifurcation diagrams to examine the dynamics of the fractional map and assess the effect of varying the fractional order. We also use the approximate entropy measure to quantify the level of chaos in the fractional map. In addition, we propose a one-dimensional stabilization controller and establish its asymptotic convergence by means of the linearization method.