Weak Signal Detection Using Chaotic Phase Transition

In this research, we conducted detailed investigations into the theory and simulation experiments of weak signal detection utilizing chaotic phase transitions. We analyzed the weak signal detection method based on oscillator initial value sensitivity and identified how transient processes impact detection performance. To address this limitation, we developed a guessing game algorithm as an improved detection approach, implementing it through careful simulation parameter tuning. Our methodology included studies on simulation input noise generation (using Gaussian noise models with adjustable variance parameters) and optimal step size selection (implemented through adaptive numerical integration algorithms). We established a comprehensive simulation model that incorporates chaotic system differential equations solved with Runge-Kutta methods. Under typical noise backgrounds characterized by specific signal-to-noise ratios, we performed detection experiments for weak sinusoidal signals. The implementation involved Fourier analysis for frequency domain characterization and phase transition threshold detection algorithms. Through these investigations, we derived valuable conclusions regarding detection sensitivity and system stability.