Chaotic characteristics of fifth nonlinear duffing system under parametric excitation

Consider the parametric excitation, studied the characteristics of fifth nonlinear duffing chaotic system. By applying geometric theory of dynamical systems, bifurcation theory and infinitesimal calculus, obtain the homoclinic orbit of fifth duffing equation. Using Melnikov method determines the initial chaotic condition of system and perturbation equation. By means of numerical calculation and computer simulation analysis, get the numerical solution, and on this basis to draw a clear chaos picture and continuous repetition of the Poincare map. Numerical simulations show that this method is an extraordinary effective method to study the fifth nonlinear duffing system.