The topological variance of neighborhood of a non-hyperbolic fixed point produced by truncation error

Abstract

In the paper,a direct evidence for truncation error to complicate a simple system is provided,which proves the existence of anti-degradation mechanism in chaotic systems. Both one-dimensional circular arc iterated system and one-dimensional parabola iterated system are constructed,respectively. In each system,there is a non-hyperbolic fixed point. The corresponding iterative sequences are theoretically proved to be simple convergent sequences. However,there are a lot of iterative sequences that could jump over the fixed point in digital experiments. It is clearly revealed by digital-cell analysis that the topological variance of neighborhood of a non-hyperbolic fixed point is produced by truncation error,either a channel of type-I intermittency or a ripple bifurcation is configured from the fixed point.