Improving Chaotic Features of Fractional Chaotic Maps

Abstract

Two fractional chaotic maps, Lu and Chen fractional chaotic maps, have been analyzed using an innovative predictor-corrector method based on a non-uniform grid. An original chaotic law to control the grid size at each iteration has been introduced. The choice of the non-uniform grid was shown to play a fundamental role to obtain chaotic behavior for a larger fractional parameter range, while decreasing the computational time. The obtained results show that the complexity of the resulting fractional chaotic system in terms of Lyapunov exponents, Fourier transforms and chaos robustness is sensitive to the choice of the grid and can be considerably improved by the proposed method.