@article{Pancoatl-Bortolotti_Enríquez-Caldera_Costa_Guerrero-Castellanos_Tello-Bello_2022, title={Liènard chaotic system based on Duffing and the Sinc function for weak signals detection}, volume={20}, url={https://latamt.ieeer9.org/index.php/transactions/article/view/6496}, abstractNote={<p>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.</p>}, number={8}, journal={IEEE Latin America Transactions}, author={Pancoatl-Bortolotti, Pedro and Enríquez-Caldera, Rogerio A. and Costa, Antonio H. and Guerrero-Castellanos, José Fermi and Tello-Bello, Maribel}, year={2022}, month={May}, pages={2114–2121} }