科研之友
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摘要
This paper presents a principle of timing-sequence geometry that is used to express any dynamic system with highly precise and dynamic properties. It provides unified theoretical support for dynamic systems of different characteristics, and it is subversive compared with the traditional and related theories. The principle uses time series that implicate dynamic characteristics as the study object , skilfully embeds critical time elements in non-uniform rational B-splines (NURBSs) through a kind of thought "timing-geometry," and obtains a "functional" relationship between geometry and time, called S-NURBS, which quantizes the nonlinear system and its dynamical properties. Two methods were provided for different research purposes. The first is the direct time NURBS method, which is appropriate for the study of the analytic properties of the dynamic system state space, and the other is the tangent vector NURBS method for the study of differential properties a system. In terms of the process of studying chaos characteristics, we proposed a new algorithm for the maximum Lyapunov exponent of chaotic time series based on the foundation of our principle. Using a few nonlinear systems, we verified the correctness and effectiveness of these methods within acceptable error limits according to the experimental results.
- 出版日期2016-4
- 单位中国科学技术大学
