A General Dynamic Model Based On Geometric Theory Of Timing Sequence

There are few effective modelling methods suitable for some complex nonlinear dynamic systems to study the motion law. However, some status data that changes over time in the dynamic motion could be obtained, called time series. As time series contains dynamic properties interior, so the dynamic features could be studied through time series. The paper mainly concerns two questions:how to depict time series for dynamic system effectively and how to research dynamic properties through time series model.The geometry modeling method NURBS is used to build free-form curve shape from a set of data points (but not limited to three-dimension and three-dimension). The set of points can be regarded as the data sequence in time series. The NURBS method could be used to depict time series, but it just uses the data sequence and ignores the time sequence. So the main issue in this paper is how to introduce time element into geometry NURBS.On the basis of the analysis above, the paper used a method of function mapping, introduced time element into the geometric model NURBS. Then, the paper presented a geometric NURBS model embedded time element (called timing geometric NURBS), which is used to describe time series and study dynamic systems. The timing NURBS is called dynamic model. Function mapping is a one-to-one correspondence between geometry modeling parameter u and time parameter t in dynamic system, denoted by u=u(t). And the paper proposed some specific exercisable mapping methods for different circumstances such as simple direct time method, complex but transformable double time method and tangent vector method for differential form.On the process of studying chaotic characters, we proposed a new algorithm for maximum Lyapunov exponent of chaotic time series on the foundation of our model. The validity of algorithm provides assistant evidence supporting the validity of our pre-sented model.In the end, according to the experimental results from a few nonlinear systems (such as projectile motion, pendulum system and Lorenz system), we verified the cor-rectness and effectiveness of these methods within acceptable error limits.