Duffing Equation for Weak Signal Detection

The Duffing equation MATLAB program for weak signal detection proves highly effective in practical applications. This implementation provides two distinct methodological approaches: one utilizing inline functions for equation definition, and another employing @fan functions for enhanced flexibility. The inline function method allows straightforward definition of the Duffing equation through direct mathematical expression input, enabling rapid computation and analysis without complex function handles. This approach is particularly suitable for quick prototyping and basic signal detection scenarios where parameter variation is minimal. The @fan function implementation offers superior flexibility for parameter adjustment and optimization procedures. This method supports dynamic parameter modification during runtime, making it ideal for adaptive signal detection algorithms and optimization routines where system parameters require frequent updating based on detection results. Both methodologies effectively facilitate weak signal detection through chaotic system characteristics. The Duffing equation's sensitivity to weak periodic signals amidst noise leverages chaotic system properties, where the system's state transition from chaotic to periodic motion indicates signal presence. Implementation typically involves solving the differential equation using numerical methods like Runge-Kutta algorithms, with phase trajectory analysis serving as the primary detection mechanism. Regardless of the chosen implementation method, this program significantly enhances research efficiency and detection accuracy in weak signal analysis applications, particularly in scenarios involving low signal-to-noise ratios where conventional detection methods prove inadequate.