A Novel Chaotic System based on Binomial Functions for Detection of Ultra Weak Signals.

This research presents a new 2nd order non-linear chaotic system that is created using the Liènard Theorem and binomial functions. The systems parameters are properly chosen to assure a stable limit cycle and simultaneously bifurcation diagrams are conjugated together with Lyapunov exponents to generate chaotic and periodic trajectories in the phase space. Then the system is configured to operate in the state of intermittence for detection of ultra-weak signals. Computer model simulations provide encouraging results for detection of signals with signal-to-noise ratio of -45 dB. As a parallel result, a new method named Short Time Inspired Lyapunov exponent (STILE), is presented as an efficient way to detect intermittence in time sequences.