PERIOD-DOUBLING ROUTE TO CHAOS AND THE POWER SPECTRUM ANALYSIS IN THE CONFINEMENT MODE TRANSITION MODELS IN NUCLEAR FUSION

Nonlinear dynamics plays a very important role in undergraduate physics education, and the power spectrum, as an important frequency domain analysis method, is often used to analyze and predict the nonlinear dynamic behavior of systems. This paper first derives the specific form of the power spectrum using the Fourier transform, and then applies it to the important model for nuclear fusion confinement mode transition—the ZCD model, observing the dynamic behavior of the system. By adjusting the amplitude of the heating power in the ZCD model and plotting the corresponding power spectrum and phase diagrams, we observe and compare the changes in the nonlinear dynamic properties of the model under different parameters. The study found that as the amplitude of the heating power increases, the turbulence intensity in the system enters chaos through a period-doubling route, making the system behavior unpredictable. During this transition, the position of the system's period-doubling bifurcation points matches the pattern described by the Feigenbaum constant.