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<p>Finding hyperchaos in simple system models is quite interesting and meaningful. This paper constructs a feasible memristive hyperchaotic map (MHM) generation framework by introducing a memristor into the newly proposed full-linear-loop map. The notable properties of MHM are that it only has a simple nonlinear term while it can generate rich dynamics. Several examples of MHMs are derived to demonstrate the effectiveness of the framework in generating MHMs. The infinitely many fixed points in MHM provide conditions for the emergence of various dynamics, whose stability is closely related to the map parameters and the initial condition of the memristor. Numerical methods are utilized to investigate the dynamics of these MHMs (such as superchaos and extreme multistability) and the complexity of hyperchaotic sequences yielded by MHM. A hardware platform based on the microcontroller is developed and the experiment outcomes confirm the physical existence of the MHMs. According to the hyperchaotic sequences generated by MHMs, some pseudo-random number generators are designed and relevant tests have demonstrated their superiority. It implies the potential of the proposed MHMs in practical applications.</p>

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Hyperchaotification of a class of full-linear-loop maps via memristor

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Minghong Qin,
  • Qiang Lai

摘要

Finding hyperchaos in simple system models is quite interesting and meaningful. This paper constructs a feasible memristive hyperchaotic map (MHM) generation framework by introducing a memristor into the newly proposed full-linear-loop map. The notable properties of MHM are that it only has a simple nonlinear term while it can generate rich dynamics. Several examples of MHMs are derived to demonstrate the effectiveness of the framework in generating MHMs. The infinitely many fixed points in MHM provide conditions for the emergence of various dynamics, whose stability is closely related to the map parameters and the initial condition of the memristor. Numerical methods are utilized to investigate the dynamics of these MHMs (such as superchaos and extreme multistability) and the complexity of hyperchaotic sequences yielded by MHM. A hardware platform based on the microcontroller is developed and the experiment outcomes confirm the physical existence of the MHMs. According to the hyperchaotic sequences generated by MHMs, some pseudo-random number generators are designed and relevant tests have demonstrated their superiority. It implies the potential of the proposed MHMs in practical applications.