Stability theory of synchronized motion in coupled-oscillator systems. II: The mapping approach. (English) Zbl 1171.70307

Yamada, Tomoji; Fujisaka, Hirokazu

Prog. Theor. Phys. 70, No. 5, 1240-1248 (1983).

Summary: 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.
For part I, cf. Prog. Theor. Phys. 69, No. 1, 32–47 (1983; Zbl 1171.70306).

MSC:

70K20	Stability for nonlinear problems in mechanics
80A30	Chemical kinetics in thermodynamics and heat transfer
93D99	Stability of control systems

Citations:

Zbl 1171.70306