A novel fractional-order hyperchaotic complex system and its synchronization

Abstract

A novel fractional-order hyperchaotic complex system is proposed by introducing the Caputo fractional-order derivative operator and a constant term to the complex simplified Lorenz system. The proposed system has different numbers of equilibria for different ranges of parameters. The dynamics of the proposed system is investigated by means of phase portraits, Lyapunov exponents, bifurcation diagrams, and basins of attraction. The results show abundant dynamical characteristics. Particularly, the phenomena of extreme multistability as well as hidden attractors are discovered. In addition, the complex generalized projective synchronization is implemented between two fractional-order hyperchaotic complex systems with different fractional orders. Based on the fractional Lyapunov stability theorem, the synchronization controllers are designed, and the theoretical results are verified and demonstrated by numerical simulations. It lays the foundation for practical applications of the proposed system.