Abstract
To analyze the periodic distribution and state-mapping structures of high-dimensional digital chaotic systems in fixed-point arithmetic domain. A chaotic cycle-finding algorithm (CCFA) can be designed to precisely calculate the period length of the orbit of digital chaos under different finite calculation accuracy. Furthermore, to test the versatility and effectiveness of our proposed algorithm, the periodic distribution and security of the digital Sprott D system are analyzed in detail. Numerical simulation results show that the chaotic system have potential security risks, such as short period and low sequence complexity. In addition, we put forward a new resistance method based on automatic cycle detection and random jump of chaotic trajectories for the objective of enhancing the dynamical properties of high-dimensional digital chaotic systems. This scheme can construct a new chaotic model with many desirable properties, such as long period, high state-space utilization, low autocorrelation, and good ergodicity.
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