The application of Melnikov function in weak signal detection with Duffing oscillators

This paper presents a new weak signal detection method with Duffing oscillators. The state transition from chaos to periodic orbit is monitored by the Melnikov function. When the Duffing oscillator is in periodic state, the Melnikov function remains zero. Otherwise, the Melnikov function will oscillate around zero. As a result, the state transition is clarified. With the aid of Melnikov function, the frequency of the weak signal is identified through the intermittent chaos phenomenon by an array of Duffing oscillator. The amplitude and the phase of a weak signal are also identified with the aid of Melnikov function plot by a Duffing oscillator array. To get the parameters, the steepest descend algorithm is used. Simulation results show the effectiveness of the proposed weak signal detection scheme.