The Study of Identification Method for Dynamic Behavior of High-Dimensional Nonlinear System

Wang Luyou,Liming Dai,Pan Fang,Mingjun Du,Yongjun Hou

doi:10.1155/2019/3497410

Abstract

The dynamic behavior of nonlinear systems can be concluded as chaos, periodicity, and the motion between chaos and periodicity; therefore, the key to study the nonlinear system is identifying dynamic behavior considering the different values of the system parameters. For the uncertainty of high-dimensional nonlinear dynamical systems, the methods for identifying the dynamics of nonlinear nonautonomous and autonomous systems are treated. In addition, the numerical methods are employed to determine the dynamic behavior and periodicity ratio of a typical hull system and Rössler dynamic system, respectively. The research findings will develop the evaluation method of dynamic characteristics for the high-dimensional nonlinear system.

Highlights

With the development of science and technology, the study to the dynamics of low-dimensional nonlinear dynamic systems can hardly satisfy the requirements of actual engineering [1, 2]
The principal method for identifying the dynamic behavior of the nonlinear system includes the Lyapunov index method, Poincaremapping method, bifurcation theory, etc. e Lyapunov index method is an important method for identifying chaotic signals of nonlinear dynamical systems. e important characteristic of the nonlinear dynamical systems is that the final value of the system is sensitively depended on the initial value; the Lyapunov index method represents the average exponential rates of divergence or convergence of closed orbits of the vibrating object in phase space of a dynamic system. e Lyapunov exponent is an efficient tool for estimating whether a dynamic system is periodic or chaotic
The Lyapunov exponent is not suitable for determining the dynamic behavior that is neither periodic nor chaotic. e Poincaremapping method can diagnose the dynamic characteristics of the nonlinear system based on the fixed points in the Poincaresection; it is unsuitable to determine the global dynamics and periodicity [6]

Summary

Introduction

With the development of science and technology, the study to the dynamics of low-dimensional nonlinear dynamic systems can hardly satisfy the requirements of actual engineering [1, 2]. In this paper, considering the principle of Poincaremapping, the periodicity ratio methods for diagnosing the dynamic characteristics of the high-dimensional nonlinear systems are proposed. According to equation (2), the overlapping points in n Poincaresections can describe the periodicity of n-dimensional nonautonomous dynamic system.

Results

Conclusion