Generalized combination complex synchronization of new hyperchaotic complex Lü-like systems

In this paper, a new hyperchaotic complex system is presented and its dynamical properties are discussed by phase portraits, bifurcation diagrams, and the Lyapunov exponents spectra. Noticeably, based on two drive complex systems and one response complex system with different dimensions, we propose generalized combination complex synchronization and design a general controller. Additionally, we investigate generalized combination complex synchronization between real systems and complex systems via two complex scaling matrices. Two examples, which include two chaotic complex systems driving one new hyperchaotic complex system and two new hyperchaotic complex systems driving one chaotic real system, are shown to demonstrate the effectiveness and feasibility of the schemes.