A novel hyperchaotic system is proposed. It is particularly interesting that the hyperchaotic system has a nonlinear term in the form of an exponential function and has onle one equilibrium. Basic dynamical properties of the hyperchaotic system are investigated. Moreover, antisynchronization of the new hyperchaotic system with parameter mismatch and external disturbances is also studied in this paper by using adaptive control. Numerical simulation results further demonstrate that the proposed methods are effective and robust.

A five-term three-dimensional (3D) autonomous chaotic system with an exponential nonlinear term is reported in this paper. Basic dynamical behaviours of the chaotic system are further investigated. Then a new synchronization phenomenon, complete switched modified function projective synchronization (CSMFPS), for this novel five-term chaotic system with uncertain parameters and disturbances is investigated. This paper extends previous work, where CSMFPS of chaotic systems means that all the state variables of the drive system synchronize with different state variables of the response system. As the synchronization scheme has many combined forms, it is a promising type of synchronization and can provide greater security in secure communication. Based on Lyapunov stability theory, a robust adaptive controller is contrived to acquire CSMFPS, parameter identification and suppress disturbances simultaneously. Finally, the Lorenz system and the new five-term chaotic system are taken as examples and the corresponding numerical simulations are presented to verify the effectiveness and feasibility of the proposed control scheme.

In our recent publication (Pramana – J. Phys. 79, 81 (2012), DOI: 10.1007/s12043-012-0285-6), our statement on adaptive antisynchronization (AS) controller design is incorrect. In this erratum we propose a correct control law. The corresponding proof is also given to demonstrate the effectiveness of the proposed control strategy.