Constructing Nonuniform Multiscroll Chaotic Strings

Traditional multiscroll chaotic attractors are typically of similar structures with uniform distribution in the phase space, which limits their application potential. Based on dynamics editing, a piecewise linear function is designed, and by tuning the slope and applying common-mode offset boosting, both uniform and nonuniform multiscroll chaotic strings with arbitrary odd or even segments are successfully coined. By adjusting the differential-mode offset boosting, a nonequidistant scroll structure is obtained, forming controllable nonuniform multiscroll chaotic strings. Waveform analysis and calculation of the maximum Lyapunov exponent demonstrate that the nonuniform multiscroll chaotic strings possess good robustness. Compared with other methods, nonuniform multiscroll chaotic strings could be defined with controllable spacing, resulting in more flexible and diverse structures. Finally, the proposed multiscroll chaotic strings are digitally implemented on the FPGA platform, verifying the corresponding methodology. These findings are of potential significance for chaos-based applications, including image encryption and secure communication.