Modifying Lyapunov exponent of chaotic map by self-cascading

The self-cascade (SC) method is an effective technique for chaos enhancement and complexity increasing in chaos maps. Additionally, the controllable self-cascade (CSC) method allows for more accurate control of Lyapunov exponents of the discrete map. In this work, the SC and CSC systems of the original map are derived, which enhance the chaotic performance while preserving the fundamental dynamical characteristics of the original map. Higher Lyapunov exponent of chaotic sequences corresponding to higher frequency are obtained in SC and CSC systems. Meanwhile, the Lyapunov exponent could be linearly controlled with greater flexibility in the CSC system. The verification of the numerical simulation and theoretical analysis is carried out based on the platform of CH32.