Quasi-chaotic mode detection and prevention in digital chaos generators

Numerical solutions of chaotic differential equations can exhibit quasi-chaotic behavior when implemented in short word length computers. Quasi-chaotic signal is a periodic waveform with extremely long period that looks chaotic on shorter time intervals. In many practical applications of chaos, it is assumed that chaotic waveform is non-recurring, thus quasi-chaotic regime is strongly undesirable. This especially affects embedded applications, where processors with short data types are common because of their low power consumption. In our work, we describe conditions under which quasi-chaotic oscillations can occur and study numerical methods from the point of robustness to the quasi-chaotic mode. An algorithm for quasi-chaotic mode detection is described. We also propose a quasi-chaotic regime elimination technique based on parameter shift approach. The simulation of Rössler chaotic system with 16-bit data representation is given as an experimental study. The obtained results show the theoretical possibility to substantially reduce the influence of the quasi-chaotic regime on low-precision chaos oscillators.