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<p>Nonlinear interactions play a crucial role in the emergence of complex dynamics, such as chaos and hyperchaos, in autonomous deterministic dynamical systems within a continuous-time framework. Investigating systems with minimal nonlinear components provides valuable insights into the fundamental mechanisms that drive chaotic behaviors. In addition, higher dimensional hyperchaotic systems have garnered significant attention due to their broad range of applications. This paper presents a 5D autonomous deterministic dynamical model in a continuous-time framework with a single nonlinearity. We investigate key dynamical properties of the system, including bifurcation analysis, Kaplan–Yorke dimension, dissipativity, equilibrium points and their stability, phase portraits, Lyapunov exponents (LEs), and Poincaré cross-sections. To achieve hybrid projective synchronization (HPS) between two identical 5D systems, we combine adaptive control with integral-based sliding mode control. The synchronization results are validated through numerical simulations in MATLAB. Finally, the practical implementation of the proposed model is demonstrated using an electronic circuit schematic with a single multiplier chip, highlighting the practical significance of the system.</p>

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A simple 5D autonomous hyperchaotic system: dynamical analysis, synchronization via adaptive integral sliding mode control, and circuit realization

  • 期刊论文

  • 发表日期：

    2025年6月19日

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  • Dinesh Khattar,
  • Naokant Deo,
  • Mukul Sirohi

摘要

Nonlinear interactions play a crucial role in the emergence of complex dynamics, such as chaos and hyperchaos, in autonomous deterministic dynamical systems within a continuous-time framework. Investigating systems with minimal nonlinear components provides valuable insights into the fundamental mechanisms that drive chaotic behaviors. In addition, higher dimensional hyperchaotic systems have garnered significant attention due to their broad range of applications. This paper presents a 5D autonomous deterministic dynamical model in a continuous-time framework with a single nonlinearity. We investigate key dynamical properties of the system, including bifurcation analysis, Kaplan–Yorke dimension, dissipativity, equilibrium points and their stability, phase portraits, Lyapunov exponents (LEs), and Poincaré cross-sections. To achieve hybrid projective synchronization (HPS) between two identical 5D systems, we combine adaptive control with integral-based sliding mode control. The synchronization results are validated through numerical simulations in MATLAB. Finally, the practical implementation of the proposed model is demonstrated using an electronic circuit schematic with a single multiplier chip, highlighting the practical significance of the system.