Abstract
Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, quantization is inevitable for digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This chapter aims at developing a novel methodology to design higher-dimensional digital chaotic systems (HDDCS) on the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy Devaney’s definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via the field programmable gate array (FPGA) platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.
Parts of this chapter were reproduced with permission from [5] \(\copyright \)IEEE 2016, [6] \(\copyright \)World Scientific Publishing Co Pte Ltd 2014, and [7] \(\copyright \)Chinese Physical Society and IOP Publishing Ltd 2015.
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Wang, Q., Yu, S., Guyeux, C. (2018). Higher-Dimensional Digital Chaotic Systems (HDDCS). In: Design of Digital Chaotic Systems Updated by Random Iterations. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-73549-8_5
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DOI: https://doi.org/10.1007/978-3-319-73549-8_5
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