Generalization of combination–combination synchronization of chaotic n-dimensional fractional-order dynamical systems

The generalization of combination–combination (C–C) synchronization of chaotic n-dimensional (nD) fractional-order (0<α≤1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(0<\alpha \le 1)$$\end{document} dynamical systems is studied. Firstly, we replace arbitrary four chaotic nD ordinary dynamical systems by four chaotic nD fractional-order dynamical systems which have unique solutions. Secondly, we extend the scheme of a recent paper (Sun et al. in Nonlinear Dyn 73: 1211–1222, 2013) to study the generalization of C–C synchronization among four nD fractional-order dynamical systems. Examples of combination–combination synchronization among four identical or different of 6D chaotic fractional-order systems are discussed. The analytical formula of the control functions is tested numerically to achieve C–C synchronization, and good agreement is found.