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A novel chaotic system in the spherical coordinates

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Abstract

Investigating new chaotic flows has been a hot topic for many years. Studying the chaotic attractors of systems with various properties illuminates a lamp to reveal the vague of the generation of chaotic attractors. A new chaotic system in the spherical coordinates is proposed in this paper. The system’s solution is inside a predefined sphere, and its attractor cannot cross the sphere. Investigation of equilibrium points of the system shows that the system has eight equilibria, and all of them are saddle. Bifurcation analysis of the system depicts the period-doubling route to chaos with changing the bifurcation parameter. Also, Lyapunov exponents in the studied interval of the bifurcation parameter are discussed. The basin of attraction of the system is investigated to show the sensitivity of the system to initial conditions.

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Author information

Authors and Affiliations

  1. School of Electrical and Information Engineering, Jiangsu University of Technology, Changzhou, 213001, P.R. China

    Lianyu Chen

  2. Department of Electronics, Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Tonantzintla, Puebla, 72840, Mexico

    Esteban Tlelo-Cuautle

  3. Department of Computer Science and Engineering, University of Kurdistan-Hewler, Erbil, Iraq

    Ibrahim Ismael Hamarash

  4. Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong district, Hanoi, 100000, Vietnam

    Viet-Thanh Pham

  5. Phenikaa Research and Technology Institute (PRATI), A&A Green Phoenix Group, 167 Hoang Ngan, Hanoi, 100000, Vietnam

    Viet-Thanh Pham

  6. Department of Electrical Engineering, Golpayegan University of Technology, Golpayegan, Iran

    Hamid Reza Abdolmohammadi

Authors
  1. Lianyu Chen
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  2. Esteban Tlelo-Cuautle
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  3. Ibrahim Ismael Hamarash
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  4. Viet-Thanh Pham
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  5. Hamid Reza Abdolmohammadi
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Correspondence to Hamid Reza Abdolmohammadi.

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Chen, L., Tlelo-Cuautle, E., Hamarash, I.I. et al. A novel chaotic system in the spherical coordinates. Eur. Phys. J. Spec. Top. 229, 1257–1263 (2020). https://doi.org/10.1140/epjst/e2020-900246-1

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  • DOI: https://doi.org/10.1140/epjst/e2020-900246-1

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