Strong nonlinear torsional vibration system of diesel shafting is studied. A dynamic model of torsional vibration system is established based on Lagrangian equation. Modified Lindstedt-Poincaré method is used to deal with primary resonance of diesel shafting torsional vibration of strong nonlinear system. Amplitude frequency response equation is obtained and influence of parameters on amplitude frequency response is analyzed. It shows that system frequency response exists jump phenomenon. As amplitude of harmonic torque decreases and damping increases, nonlinear jump of the system weakens, amplitude of the system reduces, and regions of primary resonance of the system decreases. With change of tuning parameter, amplitude excitation response has two kinds of topological structure. The result of MLP analysis is consistent with Runge Kutta numerical solutions.

3rd superharmonic resonance of a current-carrying conductor subjected to harmonic excitation and ampere force is studied. Duffing equation of the system is established by means of dynamics theory. With a method of multiple scales for nonlinear vibrations, approximate solution of 3rd superharmonic resonance is obtained. Influence of director current, alternating current, detuning, tension and excitation on the system is analyzed.

The second order Jacobian J₂ is calculated to determine the delay time T of two-dimensional reconstruction about ordinary differential equation according to the first extreme value of J₂.This method gives more information of reconstruction than orhter methods.As an example,the forced Brusselator system is discussed.

Space cells are divided by equal distance step for calculating mutual information, and delay time. This approach is simpler than that of equal probability method. Numerical results indicate that this method can determine the correct delay time, and yield the reconstructed states in the case of forced brusselator.