A relation on round-off error, attractor size and its dynamics in driven or coupled logistic map system.
In this paper, we investigate three kinds of numerical artifacts: period-like, strange-nonchaotic-attractor-like, and chaos-like behaviors in an extended logistic map system. These artificial behaviors appear in double precision and change into other real attractors in high-precision simulations. All of them are generated by a complicated dynamical process of the system and round-off truncation errors in numerical computations. A quantity beta, which is closely related to the local Lyapunov exponent, is proposed to measure the extremum of large expansion or contraction dynamical capability. Eventually, we find the artifacts will emerge if the relation is not kept: alphabeta<gamma, where gamma is the attractor size of the system and alpha is the computational precision digit, for instance, alpha=2 x 10(-16) for double precision, which has a unit round-off of 2 x 10(-16).
Shi
Pengliang
P
Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, People's Republic of China. pshi@itp.ac.cn