A universal variable extension method for designing multi-scroll/wing chaotic systems

Hairong Lin, Chunhua Wang, Yichuang Sun

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Developing a universal design method to construct different multiscroll/wing chaotic systems (MS/WCSs) has been challenging. This article proposes a general design method for MS <inline-formula><tex-math notation="LaTeX">$/$</tex-math></inline-formula> WCSs called the universal variable extension method (UVEM). It is a simple but effective approach that generates one-direction (1-D) and 2-D multiscroll/wing chaotic attractors. Using any double-scroll/wing chaotic system as the basic system, the UVEM is able to construct different MS/WCSs. Employing Chua&#x0027;s chaotic system and Lorenz chaotic system as two examples, we construct two MSCSs (including 1-D and 2-D) and two MWCSs (including 1-D and 2-D), respectively. Theoretical analysis and numerical simulation show that the constructed MS/WCSs not only can generate 1-D and 2-D multiscroll/wing chaotic attractors but also have 1-D and 2-D initial boosting behaviors. This means that the MS/WCSs designed by the UVEM are very sensitive to their initial states, and have better unpredictability and more complex chaotic behaviors. To show the simplicity of UVEM in hardware implementation, we develop a field-programmable gate array-based digital hardware platform to implement the designed MS <inline-formula><tex-math notation="LaTeX">$/$</tex-math></inline-formula> WCSs. Finally, a new pseudorandom number generator is proposed to investigate the application of the MS/WCSs. All P-values obtained by the NIST SP800-22 test are larger than 0.01, which indicates that the MS/WCSs designed by UVEM have high randomness.
Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalIEEE Transactions on Industrial Electronics
Early online date11 Aug 2023
Publication statusE-pub ahead of print - 11 Aug 2023


  • Behavioral sciences
  • Bifurcation
  • Chaotic communication
  • Chaotic system
  • Design methodology
  • Mathematical models
  • Stability analysis
  • Thermal stability
  • field-programmable gate array (FPGA) implementation
  • initial boosting behavior
  • multiscroll/wing chaotic attractors (MS/WCAs)
  • pseudorandom number generator (PRNG)


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