Strategy of numerical integral for bifurcation analysis of nonlinear system and its application

A strategy of numerical integral for bifurcation analysis of nonlinear system is introduced and the corresponding solver for periodic solution has been designed. The strategy chooses more than one phase space point as initial conditions and starts courses of numerical integral from each phase point at the same control parameter level. The periodic solver identifies the resulting steady state solutions and classifies them automatically according to the length of their periods and the topological structures of their attractors. By increasing the control parameter with a small step and repeating them above process, not only can the main branch of solution be traced, but also can the subordinate ones that exist in narrow ranges of the control parameter or have small basins of attraction be done. By use of the strategy in Holmes-Duffing equation, we found that it-is an excellent way to demonstrate and discover the, jump, symmetry breaking and other Phenomena.