A delay-disturbance method to counteract the dynamical degradation of digital chaotic systems and its application

To solve the performance degradation of chaotic system caused by computational precision limitation, a new hybrid control method is proposed by the Parameter Perturbation and Delayed Feedback (PP&DF) control. This method uses a high-performance anti-degradation pseudo-random sequence to periodically perturb the system parameters, and the output is delayed and provides feedback to the input. To verify its versatility, it is applied to low-dimensional systems and high-dimensional systems, respectively. The optimization effect is evaluated by evolution orbit, phase diagram, frequency distribution, cycle, and complexity. The analysis results show that the improved chaotic systems have good ergodicity, large period length, and high complexity at low precision. In addition, a new encryption algorithm is proposed based on the improved high-dimensional chaotic map. Compared with some of the latest encryption algorithms, it has high security level at low precision.