Detecting the State of the Duffing Oscillator by Phase Space Trajectory Autocorrelation

Detecting the state of the Duffing oscillator, a type of well-known chaotic oscillator, deeply affects the accuracy of its application. Considering this, the present paper introduced a novel method for detecting the state of the Duffing oscillator. Binary outputs, simple calculation, high precision and fast response time were the main advantages of the phase space trajectory autocorrelation. Also, this study explained the largest Lyapunov exponent as well as a number of other methods commonly employed in detecting the state of the Duffing oscillator. The precision and effectiveness of the method introduced was compared with other well-known state detection methods such as the 0-1 test and the largest Lyapunov exponent.