Recovering chaotic properties from small data

Physical properties are obviously essential to study a chaotic system that generates discrete-time signals, but recovering chaotic properties of a signal source from small data is a very troublesome work. Existing chaotic models are weak in dealing with such case in that most of them need big data to exploit those properties. In this paper, geometric theory is considered to solve this problem. We build a smooth trajectory from series to implicitly exhibit the chaotic properties with series-nonuniform rational B-spline (S-NURBS) modeling method, which is presented by our team to model slow-changing chaotic time series. As for the part of validation, we reveal how well our model recovers the properties from both the statistical and the chaotic aspects to confirm the effectiveness of the model. Finally a practical chaotic model is built up to recover the chaotic properties contained in the Musa standard dataset, which is used in analyzing software reliability, thereby further proves the high credibility of this model in practical time series. The effectiveness of the S-NURBS modeling leads us to believe that it is really a feasible and worthy research area to study chaotic systems from geometric perspective. For this reason, we reckon that we have opened up a new horizon for chaotic system research.