Two-parameter dynamics of an autonomous mechanical governor system with time delay

A deep understanding of the dynamical behavior in the parameter-state space plays a vital role in both the optimal design and motion control of mechanical systems. By combining the GPU parallel computing technique with two determinate indicators, namely the Lyapunov exponents and Poincare section, this paper presents a detailed study on the two-parameter dynamics of a mechanical governor system with different time delays. By identifying different responses in the two-parameter plane, the effect of time delay on the complexity of the evolutionary process is fully revealed. The path-following calculation scheme and time domain collocation method are used to explore the detailed bifurcation mechanisms. An interesting phenomenon that the number of intersection points of some periodic responses on the specified Poincare section differs from the actual period characteristics is found in classifying the dynamic behavior. For example, the commonly exhibited period-one orbit may have two or more intersection points on the Poincare section rather than one point. The variations of the basins of attraction are also discussed in the plane of initial history conditions to demonstrate the multistability phenomena and chaotic transitions.