Complex Behavior of a Hyperchaotic TNC Oscillator: Coexisting Bursting, Space Magnetization, Control of Multistability and Application in Image Encryption Based on DNA Coding

Abstract

In this work, several new aspects of the dynamics of the well-known TNC hyperchaotic oscillator are investigated. Numerous novelties appear in this work, namely particular structures of space magnetization, the coexistence of bursting patterns, the coexistence of up to four asymmetric different attractors, offset-boosting, and antimonotonicity. In addition to this interesting and particular combination of features in the TNC oscillator, the control of multistability phenomenon is carried out using linear augmentation control scheme. Finally, knowing that the protection of digital images is of particularly great interest, the complexity of pseudo-random hyperchaotic sequences of the TNC oscillator is combined with the similarity that the DNA coding shares with the binary code to build a new image encryption algorithm with strong robustness and high speed. This algorithm is successfully evaluated using cropping attack, noise attack and differential attack. The results obtained demonstrate that the proposed algorithm is efficient and of good quality.