The dynamic behavior of the gear train with variation of external excitation and backlash is investigated by calculating its bifurcation diagram and its maximum lyapunov exponent.

Taking the one-dimensional Logistical map and two-dimensional Henon map as example, a method obtaining bifurcation diagram of discrete systems in circuit by means of analogous components and digital components is introduced.

When subsystems are hyperchaotic, an identical system parameter is determined according to the bifurcation diagrams of the subsystems.

By the phase portrait,global bifurcation diagrams and Lyapunov exponents map,the chaos forming process of the system is studied under the presented system parameters.

By the phase portrait and the global bifurcation diagrams,the chaos forming process of the system is studied under the presented system parameters.

The amplification ratio could be more than 10~9 at any position of the diagram, so it is convenient to observe the fine structures in chaotic regions of bifurcation diagrams of the Logistic map.

Based on the theory of bifurcation and its DERPAR algorithm, the static bifurcation solution diagram of a typical twophase natural circulation system is analyzed using drift flux model, and compared with the results of homogenous model.

Bifurcations with constraints are open p roblems appeared in research on periodic bifurcations of nonlinear dynamical sys tems, but the present singularity theory doesn t contain any analytical methods and results about it.

In order to conduct research on the bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system,the vector field of the averaged equations in the form of a perturbed polynomial Hamiltonian system of degree 7 through perturbed analysis was established.