This chapter examines the generation of multiscroll chaotic attractors from fractional and fractal systems. Fractional-order systems are modified by incorporating fractal-fractional derivatives to produce self-similar chaotic dynamics. Special transformations, such as parabolic and triangular mappings, are utilized to construct various multiscroll attractors. Additionally, the chapter investigates hidden chaotic attractors within fractional-order systems, including the generalized Lorenz system, the Rabinovich-Fabrikant system, and non-smooth Chua systems. It reveals their unique properties and the coexistence of multiple attractors. These methodologies provide new insights into chaos theory and its applications in nonlinear dynamics.

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Generating Multiscroll Chaotic Attractors from Fractional-Fractal Systems

  • Jinhu Lü,
  • Xin Chen,
  • Guanrong Chen

摘要

This chapter examines the generation of multiscroll chaotic attractors from fractional and fractal systems. Fractional-order systems are modified by incorporating fractal-fractional derivatives to produce self-similar chaotic dynamics. Special transformations, such as parabolic and triangular mappings, are utilized to construct various multiscroll attractors. Additionally, the chapter investigates hidden chaotic attractors within fractional-order systems, including the generalized Lorenz system, the Rabinovich-Fabrikant system, and non-smooth Chua systems. It reveals their unique properties and the coexistence of multiple attractors. These methodologies provide new insights into chaos theory and its applications in nonlinear dynamics.