Liènard chaotic system based on Duffing and the Sinc function for weak signals detection
Keywords:
Sinc-Duffing, Liènard system, Melnikov detector, weak signal detectionAbstract
This article presents a modified Duffing system based on Liènard´s 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 Melnikov´s function that only depends on the most influential parameter in the type-Liènard 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.
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