Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. II: The Mapping Approach

The coupled-oscillator system described by differential equations is studied by a mapping. The mapping function for the coupled system is derived from the one for the uncoupled system. The bifurcation diagram is examined first by numerically integrating the coupled differential equations and second by iterating the mapping for the coupled system. Both approaches give similar results : Especially the transition from the uniform chaos to the non-uniform one occurs at the same value of the bifurcation parameter for both approaches.