"Matlab模拟复摆混沌行为研究"

This paper presents a study on the complex behavior of chaotic pendulum based on MATLAB. Chaos phenomena exist in numerous unordered, non-equilibrium, and random complex systems in nature. Chaos appears in nonlinear systems, revealing the unity of order and disorder, determinism and randomness. Chaotic motion is a unique complex motion state of nonlinear dynamic systems, characterized by seemingly random irregular motion. The discovery of chaos is regarded as the third revolution in physics after relativity and quantum mechanics, and its research has always been of great interest in the academic community. MATLAB is an excellent mathematical software that is widely used in scientific computing, engineering design, numerical analysis, and simulation analysis. The study of chaos theory involves nonlinear problems that are difficult to express analytically, and can only be solved using numerical methods, in which MATLAB excels. This paper utilizes MATLAB software to research the characteristics of classical chaotic phenomena, as well as simulate and analyze the characteristics and formation process of chaos. The chaotic behavior and phenomenon of a pendulum are simulated using MATLAB, and phase portraits and strange attractors are plotted for different periods. It can be observed that as the external driving force increases, the pendulum vibration gradually transitions from period doubling bifurcation to chaos. Keywords: chaos, MATLAB, pendulum, period doubling bifurcation, strange attractor