"基于Matlab的复摆混沌行为研究及模拟分析"

The study of chaotic behavior in complex systems has been a topic of great interest in the scientific community. Chaos phenomena can be found in various nonlinear systems, revealing a unity between order and disorder, determinism and randomness. Chaos motion is a unique and complex state of motion in nonlinear dynamical systems, characterized by seemingly random and irregular behavior. The discovery of chaos has been regarded as the third major physics revolution after relativity and quantum mechanics, attracting significant attention from researchers. Matlab is a powerful mathematical software widely used in scientific computing, engineering design, numerical analysis, and simulation analysis. Chaos theory deals with nonlinear problems that are difficult to express analytically, requiring numerical solutions for analysis. Matlab's capabilities in this regard demonstrate its strength in simulating and studying chaotic phenomena. This bachelor's thesis utilizes Matlab software to investigate the characteristics of classic chaos phenomena and simulate the characteristics and formation processes of chaos. The study also includes the simulation of chaotic behavior in a pendulum system, presenting phase portraits and strange attractors for different periods. The results show that as the external driving force increases, the pendulum vibration transitions from period doubling bifurcation to chaos. In conclusion, this research demonstrates the complex behavior of chaotic pendulum systems using Matlab, providing insights into the development and characteristics of chaos phenomena. The combination of chaos theory and Matlab software offers a powerful tool for studying nonlinear dynamics and understanding the unpredictable yet ordered nature of chaotic systems. This study contributes to the ongoing research in the field of chaos theory and nonlinear dynamics, showcasing the potential of Matlab in analyzing and simulating complex phenomena in science and engineering.