Time-Delayed Chaotic Circuit Design Using All-Pass Filter

The all-pass filter method is proposed to approximately realize time-delayed chaotic electronic circuits. The amplitude-frequency characteristic and group time delay of the all-pass filter are analyzed and compared with the known low-pass filter. The number of filters in cascade is evaluated. Using the all-pass filter method, the infinite-dimensional time-delayed nonlinear system is reduced to finite-dimensional ordinary differential equations. The corresponding time-delayed chaotic electric circuits with all-pass filters are constructed, which are experimentally proven to be effective in the range of precision. The obtained experimental results well confirm the theoretical and numerical results. The proposed method is specifically suitable for the implementation of chaotic circuits with long time delay.