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<p>This paper introduces a novel four-dimensional hyperchaotic system and conducts an in-depth analysis of its dynamical characteristics. The investigation includes the calculation of Lyapunov exponents, the generation of phase portraits and bifurcation diagrams, and the determination of the Kaplan-Yorke dimension. Additionally, the system’s equilibrium points are identified, and their stability is examined. The study further explores hybrid function projective synchronization between two identical systems, achieved through the application of adaptive control. Controllers are designed based on Lyapunov stability theory to ensure effective synchronization. Theoretical findings are validated through numerical simulations carried out using MATLAB.</p>

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Exploration of a Novel 4D Hyperchaotic System: Dynamical Insights and Advanced Synchronization via Adaptive Control

  • 期刊论文

  • 发表日期：

    2026年6月3日

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  • Govind Singh,
  • Dinesh Khattar,
  • Neha Agrawal

摘要

This paper introduces a novel four-dimensional hyperchaotic system and conducts an in-depth analysis of its dynamical characteristics. The investigation includes the calculation of Lyapunov exponents, the generation of phase portraits and bifurcation diagrams, and the determination of the Kaplan-Yorke dimension. Additionally, the system’s equilibrium points are identified, and their stability is examined. The study further explores hybrid function projective synchronization between two identical systems, achieved through the application of adaptive control. Controllers are designed based on Lyapunov stability theory to ensure effective synchronization. Theoretical findings are validated through numerical simulations carried out using MATLAB.