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<p>Multi-wing and multi-scroll hidden attractors (MW/MSHAs) have garnered significant research interest for information encryption, owing to their rich and complex dynamical behaviors. However, designing such systems is challenging due to their inherent structural complexity and the difficulty in directly controlling the number of wings or scrolls. From the above considerations, this paper proposes a novel pulse-controlled offset switching method (PCOSM) for generating both one-dimensional (1D) multi-scroll hidden attractors (MSHAs) and grid multi-scroll hidden attractors (GMSHAs). Concurrently, an improved Sprott-E system (ISES) with a single stable equilibrium point is constructed by introducing feedback into its first equation. This ISES serves as the seed system, to which the PCOSM is applied to generate the target attractors. The core mechanism of the PCOSM lies in connecting the separated hidden attractor units produced by offset boosting, which enables the flexible generation of both 1D MSHAs and GMSHAs without altering the system’s stability. Remarkably, the PCOSM enables control of the scroll number via a single modulated pulse signal, which is determined by the parameter <i>N</i>. This leads to a significant simplification in the design of complex dynamical systems. Finally, the MSHA system is implemented in both the PSpice simulation and on the Field-Programmable Gate Array (FPGA) hardware platform. Its superiority and physical realizability are validated through complexity comparison analysis and pseudo-random number testing, demonstrating the effectiveness of the PCOSM.</p>

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Offset switching for generating multi-scroll hidden attractors with only stable equilibria

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Xiaoyu Hu,
  • Panpan Wu,
  • Hong Wang,
  • Hongbo Cao

摘要

Multi-wing and multi-scroll hidden attractors (MW/MSHAs) have garnered significant research interest for information encryption, owing to their rich and complex dynamical behaviors. However, designing such systems is challenging due to their inherent structural complexity and the difficulty in directly controlling the number of wings or scrolls. From the above considerations, this paper proposes a novel pulse-controlled offset switching method (PCOSM) for generating both one-dimensional (1D) multi-scroll hidden attractors (MSHAs) and grid multi-scroll hidden attractors (GMSHAs). Concurrently, an improved Sprott-E system (ISES) with a single stable equilibrium point is constructed by introducing feedback into its first equation. This ISES serves as the seed system, to which the PCOSM is applied to generate the target attractors. The core mechanism of the PCOSM lies in connecting the separated hidden attractor units produced by offset boosting, which enables the flexible generation of both 1D MSHAs and GMSHAs without altering the system’s stability. Remarkably, the PCOSM enables control of the scroll number via a single modulated pulse signal, which is determined by the parameter N. This leads to a significant simplification in the design of complex dynamical systems. Finally, the MSHA system is implemented in both the PSpice simulation and on the Field-Programmable Gate Array (FPGA) hardware platform. Its superiority and physical realizability are validated through complexity comparison analysis and pseudo-random number testing, demonstrating the effectiveness of the PCOSM.