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Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot

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  • Nwachioma, Christian
  • Pérez-Cruz, J. Humberto

Abstract

This paper presents a new chaotic system that has four attractors including two fixed point attractors and two symmetrical chaotic strange attractors. Dynamical properties of the system, viz. sensitive dependence on initial condition, Lyapunov spectrum, measure of strangeness, basin of attraction including the class and size of it, existence of strange attractor, bifurcation analysis, multistability, electronic circuit design, and hardware implementation are rigorously treated. It is found by numerical computations that the system has a far-reaching composite basin of attraction, which is important for engineering applications. Moreover, a circuit model of the system is realized using analog electronic components. A procedure is detailed for converting the system parameters into corresponding values of electronic components such as the circuital resistances while ensuring the dynamic ranges are well contained. Besides, the system is used as the source of control inputs for independent navigation of a differential drive mobile robot, which is subject to the Pfaffian velocity constraint. Due to innate properties of the system such as sensitivity on initial condition and topological mixing, the robot’s path becomes unpredictable and guaranteed to scan the workspace, respectively.

Suggested Citation

  • Nwachioma, Christian & Pérez-Cruz, J. Humberto, 2021. "Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000370
    DOI: 10.1016/j.chaos.2021.110684
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    References listed on IDEAS

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    1. J. Humberto Pérez-Cruz & Jacobo Marcos Allende Peña & Christian Nwachioma & Jose de Jesus Rubio & Jaime Pacheco & Jesus Alberto Meda-Campaña & David Ávila-González & Olivia Guevara Galindo & Ignacio A, 2020. "A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System," Complexity, Hindawi, vol. 2020, pages 1-12, July.
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    7. Rodrigo Méndez-Ramírez & Adrian Arellano-Delgado & César Cruz-Hernández & Rigoberto Martínez-Clark, 2017. "A New Simple Chaotic Lorenz-Type System and Its Digital Realization Using a TFT Touch-Screen Display Embedded System," Complexity, Hindawi, vol. 2017, pages 1-13, July.
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    Cited by:

    1. Yang, Yu & Qin, Shijie & Liao, Shijun, 2023. "Ultra-chaos of a mobile robot: A higher disorder than normal-chaos," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Li, Peiluan & Han, Liqin & Xu, Changjin & Peng, Xueqing & Rahman, Mati ur & Shi, Sairu, 2023. "Dynamical properties of a meminductor chaotic system with fractal–fractional power law operator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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