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A flexible chaotic system with adjustable amplitude, largest Lyapunov exponent, and local Kaplan–Yorke dimension and its usage in engineering applications

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Abstract

Designing and analyzing new chaotic systems with desired properties has gotten much interest recently. Through applying modification in a recent rare chaotic flow which has adjustable Kaplan–Yorke dimension, a flexible chaotic system is introduced in this work. In the mentioned modification, two parameters are added which can control amplitude of the attractor and largest Lyapunov exponent. Statistical and dynamical properties of such system could be discovered by applying stability analysis, estimating Lyapunov exponents, local Kaplan–Yorke dimension, and plots of state space. Interestingly, this system is in group of systems which have coexisting attractors, so it is a multistable chaotic system. By considering a practical application of this rare system, meaningful relation between the value of local Kaplan–Yorke dimension and the ability of the system as a random number generator can be seen in statistical tests.

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Acknowledgements

Sajad Jafari and Atiyeh Bayani were supported by Iran National Science Foundation (No. 96000815). The work was supported by the Natural Science Foundation of China (No. 11726624), the Natural Science Basic Research Plan in Shandong Province of China (No. ZR2017PA008), Science and Technology Program of Xi’an (No. 2017134SF/WM028).

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Authors and Affiliations

  1. Research and Development Center of Intelligent Control Technology, School of Science, Xijing University, Xi’an, 710123, China

    Heng Chen

  2. Shaanxi Engineering Research Center of Controllable Neutron Source, School of Science, Xijing University, Xi’an, 710123, China

    Heng Chen

  3. Biomedical Engineering Department, Amirkabir University of Technology, Tehran, 15875-4413, Iran

    Atiyeh Bayani & Sajad Jafari

  4. Department of Electrical and Electronic Engineering, Faculty of Technology, Sakarya University, Adapazari, Turkey

    Akif Akgul

  5. Institute for Advanced Study, Shenzhen University, Guangdong, 518060, China

    Mohammad-Ali Jafari & Xiong Wang

  6. Biomedical Engineering Department, Qazvin Islamic Azad University, Qazvin, Iran

    Mohammad-Ali Jafari

  7. School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

    Viet-Thanh Pham

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  1. Heng Chen
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  2. Atiyeh Bayani
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  3. Akif Akgul
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  7. Sajad Jafari
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Correspondence to Sajad Jafari.

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Chen, H., Bayani, A., Akgul, A. et al. A flexible chaotic system with adjustable amplitude, largest Lyapunov exponent, and local Kaplan–Yorke dimension and its usage in engineering applications. Nonlinear Dyn 92, 1791–1800 (2018). https://doi.org/10.1007/s11071-018-4162-9

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  • DOI: https://doi.org/10.1007/s11071-018-4162-9

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