A Three-Dimensional Autonomous System with a Parabolic Equilibrium: Dynamical Analysis, Adaptive Synchronization via Relay Coupling, and Applications to Steganography and Chaos Encryption

This paper is reporting on electronic implementation of a three-dimensional autonomous system with infinite equilibrium point belonging to a parabola. Performance analysis of an adaptive synchronization via relay coupling and a hybrid steganography chaos encryption application are provided. Besides striking parabolic equilibrium, the proposed three-dimensional autonomous system also exhibits hidden chaotic oscillations as well as hidden chaotic bursting oscillations. Electronic implementation of the hidden chaotic behaviors is done to confirm their physical existence. A good qualitative agreement is shown between numerical simulations and OrCAD-PSpice results. Moreover, adaptive synchronization via relay coupling of three three-dimensional autonomous systems with a parabolic equilibrium is analysed by using time histories. Numerical results demonstrate that global synchronization is achieved between the three units. Finally, chaotic behavior found is exploited to provide a suitable text encryption scheme by hidden secret message inside an image using steganography and chaos encryption.