Study on the dynamic behavior of truncation errors in non-hyperbolic fixed points chaotic systems

It is always thought that discrete dynamical systems were collapsed from complicated long period to simple short period by computer truncation errors. In this paper, a system induced to complication completely by computer truncation is offered. The theoretical solution is a convergent sequence and the corresponding computer solution is a diverging system. Analysis shows that it's the computer truncation error that makes the system performance changes. This anti-degradation mechanism can be applied to chaotic encryption, which will solve the weak key problem caused by the collapse of chaotic system.