Chaos and bifurcation analysis of Chua's circuit

• Main Authors: Wey, Yan Yih, 魏巖懿
• Other Authors: Twu, Shih Hsiung
• Format: Others
• Language: zh-TW
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/63325451434107005068

碩士 === 中原大學 === 電機工程研究所 === 82 === In the thesis, we study the chaos and bifurcations in Chua's circuit by theoretical analysis and simulations. Chua's circuit is now one of the most well - known and extensively investigated dynamic systems. It exhibits an immensely rich chaotic phenomena and bifurcation processes, especially in the parameter region : the double scroll family. The dynamic equation of Chua's circuit is a third - order differential equation. However, we will analyze the dynamics of Chua's circuit in the double scroll family by using the geometrical methods. At first, for every fixed parameter, the one -dimensional Poincare map can be obtained from two half- Poincare maps that represent the typical trajectories in geometrical structure of Chua's circuit. Then, in new transformed coordinate systems, we calculate the accurate solutions of the Poincare maps by applying the theory of confinors in a particular range of parameter space. Finally, the resulted Poincare maps will be used to construct the precise bifurcation diagrams when one parameter is varied. There are four main results are found from the precise bifurcation diagrams :（１）The chaotic behavior exists in a wide parameter region. （２）The coexistence of two attractors occurs. It can be concluded that the corresponding Poincare maps are multimodal.（３）The phenomenon of period - bubbling bifurcation patterns happen. It is obtained from the magnified bifurcation processes.（４）The 1 - D Poincare maps exhibit complex shapes as the parameter is varied in the chaotic regions. These shapes indicate that the Poincare maps are very sensitive to the previous state.