AI Article Synopsis
- The paper explores a new fractional order chaotic map that shows chaotic behavior without a fixed point, marking a first in this area of study.
- Researchers use phase plots, bifurcation diagrams, and approximate entropy to analyze the dynamics of the fractional map and how changing the fractional order affects chaos levels.
- A one-dimensional stabilization controller is proposed, and its effectiveness is validated through a linearization method showing it can achieve asymptotic convergence.
Article Abstract
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.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512281 | PMC |
| http://dx.doi.org/10.3390/e20100720 | DOI Listing |
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