Duffing Oscillator-Based Weak Signal Frequency Detection

This MATLAB program implements weak signal frequency detection using Duffing oscillators. The system employs chaotic resonance principles where the oscillator's state transition threshold is sensitive to specific frequency components. Key algorithmic features include: - Phase space trajectory analysis to identify frequency matches - Bisection method for precise frequency resolution within ±0.03 range - Adaptive noise filtering achieving -68dB SNR through wavelet denoising and correlation detection The implementation calculates Lyapunov exponents to determine oscillator stability transitions when weak signals match the driving frequency. Signal processing chains incorporate Hilbert transforms for instantaneous frequency measurement and autocorrelation for noise suppression. The dual-oscillator configuration compares chaotic and periodic states through Poincaré mapping, enabling reliable detection even with substantial background interference.