| The degradation of digital chaos is always a hot research issue related to many practical applications of basic research and applied basic research in chaos theory. Based on the dynamical properties of chaos system and the features of its digitalization, we will make a thorough research on the property of discrete dynamical systems in the neighborhood of the fixed point under the influence of computing error. Here we provide a preliminary discussion of anti-degradation mechanism based on the effect of computing error, which makes some theoretically simple convergent systems divergent and complex. A concept of Computing Instability (CI) is proposed to analyze and measure the anti-degradation ability of a system, which is used to prove the fact that only the Saddle Point (SP) and 3rd class of the Non-Hyperbolic Fixed Point (NHFP3) have the property of CI. Then we will construct NHFP3 systems, the Arc Iterative System and Parabolic Iterative System, both of which are theoretically convergent while the iterative sequences that could jump over the fixed point are found in the corresponding numerical experiment. The "Cellular" method helps to show the variation clearly the 1st class of intermittency chaos and ripple bifurcation will be formed. As an example of SP system, a sequence which has a seed on the attractive branch of the SP should converge to the fixed point, but during the numerical experiment, the sequence will be divergent to 2 different divergent directions of the system with a certain probability regardless of the calculation precision. It is also illustrated by a theoretically convergent sequence near SP of the Henon system, which falls in the chaotic attractor eventually in experiment. As the consequence, the existence of the anti-degradation phenomenon is confirmed and the NHFP3 or SP property is a necessary condition of the anti-degradation system, which provides both theoretical and experimental support for the further study of the anti-degradation mechanism in chaos. |
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