期刊
MATHEMATICAL BIOSCIENCES AND ENGINEERING
卷 19, 期 3, 页码 2489-2505出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2022115
关键词
nonlinear dynamics; chaotic map; stability; maximal lyapunov exponent; entropy
资金
- OST.IM Technical University
This paper presents a new one-dimensional chaotic map K(x) = mu x(1 -x) and analyzes its dynamical properties and comparison with the traditional logistic map. The results show that this map has a larger range of stability and chaos, which may achieve better results in the fields where the logistic map has been used before.
In this paper, a novel one dimensional chaotic map K(x) = mu x(1 -x) posed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.
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