On fractional coupled logistic maps: chaos analysis and fractal control

Abstract

This paper investigates chaotic and fractal dynamics of fractional coupled logistic maps constructed based on the Caputo fractional h-difference. The chaos of this map, affected by the memory and scale derived from the fractional operator, is examined through phase portrait, “0–1” test and Lyapunov exponent. Fractal synchronization is achieved by designing a coupled controller between Julia sets generated from two fractional coupled maps with different structures. Numerical simulations are presented to validate the main findings.