Theory and Simulation Experiments of Weak Signal Detection Using Chaotic Phase Transition

Through theoretical research and simulation experiments on weak signal detection utilizing chaotic phase transition, we analyzed the method based on oscillator initial value sensitivity for detecting weak signals. Our findings indicate that transient processes significantly impact detection performance. Consequently, we proposed an enhanced weak signal detection algorithm incorporating optimized parameter tuning and noise handling techniques. After thorough investigation of simulation input noise generation (implemented using random number generators with specific probability distributions) and simulation step size selection (optimized through iterative convergence testing), we constructed a robust simulation model. This model employs numerical integration methods like Runge-Kutta algorithms to simulate chaotic oscillator dynamics. Experimental verification was conducted by detecting weak sinusoidal signals embedded in typical noise backgrounds, including white Gaussian noise and colored noise environments. The improved methodology enhances weak signal detection effectiveness, enabling more accurate signal analysis and identification through advanced signal processing algorithms. By studying transient processes, we gained deeper insights into how oscillator initial value sensitivity influences weak signal detection mechanisms. Simultaneously, by optimizing simulation parameters including noise generation functions and adaptive step-size control algorithms, we achieved more realistic simulations of practical signal detection scenarios. This research holds significant importance for profoundly understanding the principles and applications of weak signal detection methods. Future studies may explore additional algorithmic enhancements, such as machine learning-based noise filtering or multi-oscillator array configurations, to further improve detection accuracy and reliability under complex noise conditions.