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In 2019, Zhang and Zeng reported a 3-D chaotic jerk system with no equilibrium point. In this research work, we modify the dynamics of Zhang-Zheng chaotic jerk system (2019) and obtain a new chaotic jerk system with no equilibrium point. Since the new chaotic jerk system has no equilibrium point, it exhibits hidden attractors. We carry out a detailed bifurcation analysis involving bifurcation diagrams and Lyapunov exponents for the proposed no-equilibrium chaotic jerk system. We also derive new results for the coexisting attractors for the proposed no-equilibrium chaotic jerk system. We apply backstepping control to derive new results for the synchronization of a pair of new chaotic jerk systems taken as the master and slave systems. We derive a secure communication application, viz. chaotic masking, as an application of the synchronization design.

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A New No-Equilibrium Chaotic Jerk System, Its Bifurcation Analysis and Synchronization

  • 会议论文

  • 发表日期：

    2025年

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  • Sundarapandian Vaidyanathan,
  • Fareh Hannachi,
  • Mohamad Afendee Mohamed,
  • Aceng Sambas

摘要

In 2019, Zhang and Zeng reported a 3-D chaotic jerk system with no equilibrium point. In this research work, we modify the dynamics of Zhang-Zheng chaotic jerk system (2019) and obtain a new chaotic jerk system with no equilibrium point. Since the new chaotic jerk system has no equilibrium point, it exhibits hidden attractors. We carry out a detailed bifurcation analysis involving bifurcation diagrams and Lyapunov exponents for the proposed no-equilibrium chaotic jerk system. We also derive new results for the coexisting attractors for the proposed no-equilibrium chaotic jerk system. We apply backstepping control to derive new results for the synchronization of a pair of new chaotic jerk systems taken as the master and slave systems. We derive a secure communication application, viz. chaotic masking, as an application of the synchronization design.