Complete chaos synchronization of six-term Sundarapandian chaotic systems with exponential nonlinearity via active and adaptive control

Recently, a new six-term 3-D chaotic system with an exponential nonlinearity was discovered (Sundarapandian, 2013). This novel chaotic system has two saddle focus nodes and hence they are unstable. The maximal Lyapunov exponent (MLE) for the six-term Sundarapandian chaotic system was found as 3.2827 and the Lyapunov dimension of the Sundarapandian chaotic system was found as D_L = 2.1668. Complete synchronization of chaotic systems deals with the problem of asymptotically synchronizing the states of a pair of chaotic systems called as master and slave systems with the help of controllers attached to the slave system. Complete synchronization of chaotic systems has applications in many engineering areas such as secure communications, secure data encryption, cryptosystems, etc. This paper addresses the design of active and adaptive feedback controllers for completely synchronizing the states of identical six-term Sundarapandian chaotic systems with exponential nonlinearity. Active controllers are used when the system parameters a, b and c are available for measurement and the synchronization result is established using Lyapunov stability theory. Numerical simulations using MATLAB have been shown to demonstrate the proposed active and adaptive synchronization results for the novel chaotic system discussed in this paper.