The Influence of the Wavelet Transform Method on Master Stability Functions in Nonlinear Coupled Chaotic Systems

• Main Author: 李家緯
• Other Authors: 李金龍
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/21694716487382248589

碩士 === 國立新竹教育大學 === 應用數學系碩士班 === 103 === Abstract The largest Lyapunov exponent of the synchronization manifold in coupled chaotic systems is called the master stability function MSF. MSF is an effective tool to study the synchronous phenomena in coupled chaotic systems. In this thesis, the influence of the wavelet transform method on MSFs are discussed for the coupling matrix G with periodic boundary conditions. First, we clarify a necessary and sufficient condition for local synchronized in coupled chaotic systems. Moreover, the synchronous interval is analytically indicated for coupled chaotic systems. Then, the four typical nonlinear coupled chaotic systems: Rössler system, Lorenz System, Chua's Circuit System, and HR Neuron are numerically presented to verify our theoretical results for several oscillators with periodic boundary conditions. Finally, the wavelet parameter α is selected to illustrate its corresponding synchronous interval.