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.

中文翻译：

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超混沌 TNC 振荡器的复杂行为：共存爆发、空间磁化、多稳态控制及其在基于 DNA 编码的图像加密中的应用

在这项工作中，研究了著名的 TNC 超混沌振荡器动力学的几个新方面。这项工作出现了许多新颖性，即空间磁化的特定结构、爆发模式的共存、多达四个不对称不同吸引子的共存、偏移增强和反单调性。除了 TNC 振荡器中这种有趣且特殊的特征组合外，多稳态现象的控制是使用线性增强控制方案进行的。最后，知道数字图像的保护特别重要，将TNC振荡器伪随机超混沌序列的复杂性与DNA编码与二进制编码的相似性相结合，构建了一种鲁棒性强、速度快的新型图像加密算法。使用裁剪攻击、噪声攻击和差分攻击对该算法进行了成功的评估。所得结果表明，所提出的算法是高效且质量好的。