A Universal Variable Extension Method for Designing Multiscroll/Wing Chaotic Systems
Hairong Lin, Chunhua Wang, Yichuang Sun
Abstract
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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><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'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 xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><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.