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<p>Developing a universal and straightforward design methodology for constructing grid multiwing/multiscroll chaotic systems (GMW/MSCSs) with precisely controllable attractor position, amplitude, and numbers remains challenging. This paper introduces a novel generalized extension method for multiwing/scroll chaotic attractors (EMMCA). Utilizing one single piecewise linear function, EMMCA constructs a concise and efficient framework for systematically generating one-dimensional (1D-), 2D-, and 3D-MW/MSCSs from seed systems. To verify validity and generality, EMMCA was applied to five distinct chaotic systems (both 3D and 4D cases). Specifically, implementation of the modified Sprott B system generated 1D-MWCS, 2D-GMWCS, and 3D-GMWCS, and comprehensive dynamic analyses (phase diagrams, Lyapunov exponents, bifurcation diagrams, and time series) were performed. In addition, these systems exhibit amplitude control and unique directed offset boosting behavior. Notably, directed offset boosting can be adjusted deterministically with parameters or initial conditions and can be manifested in four directions simultaneously. Moreover, experimental validation via the field-programmable gate array (FPGA) platform confirmed the physical realizability of the proposed MW/MSCSs. Finally, to demonstrate application potential, a pseudo-random number generator (PRNG) and a simple-structure image encryption scheme utilizing the proposed chaotic systems were designed, both of which exhibit good security performance.</p>

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Generalized extension method for grid multiwing/scroll chaotic attractors with directed offset boosting based on one single function: design, dynamic analysis and FPGA implementation

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • Jian Zeng,
  • Qun Ding

摘要

Developing a universal and straightforward design methodology for constructing grid multiwing/multiscroll chaotic systems (GMW/MSCSs) with precisely controllable attractor position, amplitude, and numbers remains challenging. This paper introduces a novel generalized extension method for multiwing/scroll chaotic attractors (EMMCA). Utilizing one single piecewise linear function, EMMCA constructs a concise and efficient framework for systematically generating one-dimensional (1D-), 2D-, and 3D-MW/MSCSs from seed systems. To verify validity and generality, EMMCA was applied to five distinct chaotic systems (both 3D and 4D cases). Specifically, implementation of the modified Sprott B system generated 1D-MWCS, 2D-GMWCS, and 3D-GMWCS, and comprehensive dynamic analyses (phase diagrams, Lyapunov exponents, bifurcation diagrams, and time series) were performed. In addition, these systems exhibit amplitude control and unique directed offset boosting behavior. Notably, directed offset boosting can be adjusted deterministically with parameters or initial conditions and can be manifested in four directions simultaneously. Moreover, experimental validation via the field-programmable gate array (FPGA) platform confirmed the physical realizability of the proposed MW/MSCSs. Finally, to demonstrate application potential, a pseudo-random number generator (PRNG) and a simple-structure image encryption scheme utilizing the proposed chaotic systems were designed, both of which exhibit good security performance.