Nonlinear analysis of high accuracy and reliability in traffic flow prediction

For quantitatively identifying the chaotic patterns in traffic flow prediction, certain types of Duffing systems can be used. The accuracy and reliability of numerical results of the system's solution have significant influence on the traffic flow prediction. The nonlinear dynamic behavior of Duffing system used for the traffic flow prediction is investigated in this research. The solutions of the system are developed and solved numerically by using the P-T method. The regular and irregular responses of the system considered are graphically illustrated with the newly developed P-R method. Based on the results of the research, the frequency and amplitude of the external excitations applied on the system significantly affecting the nonlinear dynamic behavior therefore the traffic flow prediction in transferring the results by Wigner-Ville transform. Additionally, a comparison between the P-T and Runge-Kutta method is conducted in regarding the accuracy and reliability of the methods.