Time-frequency high-resolution for weak signal detection using chaotic intermittence[Formula presented]

Background: A non-linear Liènard-type system based on trigonometric functions is designed and used as a highly sensitive signal detector. Based on the intermittence mechanism presented in some chaotic systems, an adaptive detection array built by five chaotic oscillators is fully tuned and tested. In the array, each oscillator identifies changes in frequency for non-stationary weak signals and gives an estimate of the timing at which intermittence occurred, allowing the representation of a time-frequency spectrogram even when high-level noise is present. Methods: This work shows that the trigonometric-based system has an asymptotically stable limit cycle centered at the origin through two methods: first under the fixed-point analysis and later by the Melnikov method, which uses a family of periodic orbits. Once the limit cycle is assured, through an iterative method for searching and tuning parameters, the system is configured to drive itself into the route to chaos named intermittence. Then, the new system can be used as a non-stationary signal detector that simultaneously provides high-resolution time-frequency representation. Results: Computer experiments showed that our trigonometric oscillator when working in the chaotic intermittence regime and configured as an adaptive array, overcomes the SNR threshold present in other second-order non-linear oscillators such as Duffing, Van der Pol, and Van der Pol-Duffing, achieving high detection rates under noisy conditions, and maintaining a relative error of around 1% with -35 dB SNR. Conclusions: Our oscillator provides better sensitivity to small signals as well as noise rejection, in comparison with traditional oscillators. Furthermore, our entire system formed by a Liènard-type five-oscillator array promises to detect low-power signals and their TF reconstruction with a minimum error.