Lienard chaotic system based on Duffing and the Sinc function for weak signals detection

This article presents a modified Duffing system based on Lienards Theorem and the integral of Melnikov, the first is used to propose the interpolation Sinc as a non-linear damping function and the second is used to assure an asymptotically stable limit cycle. The Sin-Duffing system is driven into chaos by using its corresponding bifurcation diagram, Lyapunov exponents, and the Theory of Melnikov. Furthermore, the system is placed in a critical state which produced chaotic and periodic sequences, driving it into a regimen of intermittence between chaos and the self-sustained oscillations near the stable limit cycle. Intermittence is achieved by searching and tuning all involved parameters when a very systematic procedure is used. Also, such a regimen is presented here as a useful mechanism to estimate the frequency of a very low weak signal for detection applications. The latest is made possible because the system capabilities to distinguish the intermittent periods were strengthened by a new method based on Melnikovs function that only depends on the most influential parameter in the type-Lienard system. The complete system formed by the new Sinc-Duffing oscillator showed higher sensitivity compere to other chaotic systems such as the traditional Duffing or the Van der Pol-Duffing for weak signal detection with a signal-to-noise ratio down to -70 dB.