| After entering the 21st century, both of the theory and application in nonlinear dynamics have made great progress. This has prompted a growing number of scholars solving problems based on nonlinear dynamics-viewpoint. They applied the mathematical model of nonlinear systems,engineering sciences, life sciences, social sciences and other fields to predict the long-term dynamics and reveal the inherent regularity. Spring system, an important nonlinear reserach subject, has been more and more widely used in many area of mechanical engineering, such as vehicle engineering, vehicle suspension and vibration field, and, high-speed transmission area of aircraft engine. This paper is mainly to discuss the complexity of movement on two types of composite spring system.This thesis is divided into two parts. The first part is to establish two classes of dynamics of a class of composite spring mathematical modeling are discussed, the stability of the dynamics are analyzed; In the second part, the mathematical modeling of a class of composite spring oscillators is proposed, the complexity of traveling wave solutions of the system is analyzed.The main contents and results are included in the following two aspects:(1) According to the motion characteristics of spring oscillators a class of composite spring system equations of motion model is established, using Liapunova function method to analyze the stability of the two movement of the system.(2) The mathematical modeling of a class of composite spring oscillators is proposed, the complexity of traveling wave solutions of the system is analyzed. Based on Melnikov function method, it is proved that the traveling wave solutions of the system can appear Smale horseshoe chaos; By KAM theory and the cycle-energy relations of plane Hamilton system, quasi-periodic motion of the system can occur near the center of the system.
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