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Dynamical degradation is a known problem in the computer simulation of chaotic systems. Data type limitations, sampling, and rounding errors give rise to the periodic behavior. In applications of chaotic systems in secure communication and cryptography systems, such effects can reduce data storage security and operation. In this study, we considered a possible solution to this problem by using semi-explicit integration. The key idea is to perturb the chaotic trajectory by switching between two integrators, which possess close but still different numerical solutions. Compared with the traditional approach based on the perturbation of the bifurcation parameter, this technique does not significantly change the nonlinear properties of the system. We verify the efficiency of the proposed perturbation method through several numerical experiments using the well-known Rössler oscillator.

Avoiding Dynamical Degradation in Computer Simulation of Chaotic Systems Using Semi-Explicit Integration: Rössler Oscillator Case