In this paper, we investigate the finite-time synchronization problem of a novel hyperchaotic complex-variable system which generates 2-, 3-and 4-scroll attractors. Based on the finite-time stability theory, two control strategies are proposed to realize synchronization of the novel hyperchaotic complex-variable system in finite time. Finally, two numerical examples have been provided to illustrate the effectiveness of the theoretical analysis.

This paper investigates the combination-combination synchronization of four nonlinear complex chaotic systems. Based on the Lyapunov stability theory, corresponding controllers to achieve combination-combination synchronization among four different nonlinear complex chaotic systems are derived. The special cases, such as combination synchronization and projective synchronization, are studied as well. Numerical simulations are given to illustrate the theoretical analysis.

This paper investigates the synchronization and antisynchronization problems of a hyperchaotic complex Chen system with unknown parameters based on the properties of a passive system. The essential conditions are derived under which the synchronization or antisynchronization error dynamical system could be equivalent to a passive system and be globally asymptotically stabilized at a zero equilibrium point via smooth state feedback. Corresponding parameter estimation update laws are obtained to estimate the unknown parameters as well. Numerical simulations verify the effectiveness of the theoretical analysis.

In this paper, we investigate adaptive switched generalized function projective synchronization between two new different hyperchaotic systems with unknown parameters, which is an extension of the switched modified function projective synchronization scheme. Based on the Lyapunov stability theory, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve adaptive switched generalized function projective synchronization between two different hyperchaotic systems. A numerical simulation is conducted to illustrate the validity and feasibility of the proposed synchronization scheme.

We investigate the adaptive hybrid synchronization problem for a new hyperchaotic system with uncertain parameters. Based on the passivity theory and the adaptive control theory, corresponding controllers and parameter estimation update laws are proposed to achieve hybrid synchronization between two identical uncertain hyperchaotic systems with different initial values, respectively. Numerical simulation indicates that the presented methods work effectively.