At present, commonly used methods of weak signal detection such as the wavelet threshold denoising method, digital filtering method, the Fourier frequency domain transformation etc. can achieve the lowest detection of signal-to-noise ratio (SNR) of -10 dB, and the bidirectional ring coupled Duffing oscillator can reach the lowest detected SNR of -20 dB. But the discharge pulse signal with a lower SNR often appears in on-site testing, so the existing detection methods are difficult to meet the practical requirements of weak signal detection. In order to effectively solve the problem, a new method for weak pulse signal detection is proposed based on an extended-Duffing oscillator. The main idea of this method is to make the Duffing oscillator model transform to an extended-Duffing oscillator model by using the general time scale transformation. This approach can effectively expand the frequency detection range for weak signal detection. In addition, because the critical amplitude of the Duffing system depends on various parameters, such as system parameters, initial values, driving signal frequency, and calculation step of Runge - Kutta method etc.. However, the Melnikov method is an approximate analytical method, which does not take into account the factors such as initial values and calculation step, therefore, the Melnikov method is not suitable for numerical simulations, and lack of practicality. For this, the critical amplitude of chaos with high accuracy is determined only through the simulation experiment. Experimental results show that the critical amplitude is equal to 0.825010 when the incentive angular frequency of the extended-Duffing oscillator equals 10000 rad/s, and the extended-Duffing oscillator changes from the critical chaotic state to the large scale cycle state for small changes (10-6) of the driving amplitude. The simulation results show that the extended-Duffing oscillator not only has a good noise immunity performance, but also can effectively detect weak partial discharge pulse signal so that the signal-to-noise ratio can be lower than -40 dB. This method further expands the detection range and application fields of weak signals.