A modified coupled map car-following model is proposed for a one-way with the application of intelligent transportation system to describe the dynamic characteristics of one-way traffic flow and the control of traffic congestion. Based on the present model and the theory of feedback control，the stability criteria are given for the change of speed of the lead vehicle. The theoretical analysis shows that the information on more leading vehicles of each vehicle could lead to a stabilization effect for the traffic flow，that is，the stability conditions could be considerably weakened. The corresponding numerical simulations confirm the correctness of the theoretical analysis. Through comparing the present results with those in previous works，it is concluded that the proposed control strategy is more effective in suppressing the formation of traffic congestion by applying and controlling the induction information provided by the intelligent transportation system.

Using the homotopy analysis method (HAM), the nonlinear equation of the jamming transition problem (JTP) in traffic flow is discussed, which is based on the Lorentz system. Through choosing different initial approximation solutions and different linear operators, approximation solutions of the JTP and the corresponding residual errors are obtained respectively. By comparing the present results with the previous related studies, the following conclusions can be drawn that the HAM is superior to the differential transform method; however, a linear operator should be chosen as best you can to approach the linear part of the original operator in using the HAM. A new method to choose the initial approximation solution (named double HAM) is given. The correctness of the theoretical analysis is verified by numerical simulation.

A class of nonlinear generalized Duffing equation for disturbed oscillator is considered. Firstly, the typical Duffing equation is solved. Then approximate solutions to the nonlinear Duffing equation for disturbed oscillators in stochastic resonance is obtained using the generalized functional variation principle, and the uniform validity is proved.

Using the homotopic theory, an approximate solution for a class of nonlinear pro blems is first discussed.Then,the precision is raised by using variational inter active methods.Finally, a combustion model is applied and the approximate soluti on is obtained.