This chapter investigates multimode oscillations and localized oscillation modes in inductor-coupled hard oscillators, which are considered as a form of a van der Pol oscillators with relatively higher-order nonlinearity. First, the method of averaging for weakly nonlinear oscillators is surveyed. Then, the averaged equation of the two inductor-coupled oscillators is derived. In particular, we show that a double-mode oscillation is stably excited in the coupled system for weakly nonlinear oscillators. When the nonlinearity of the coupled system becomes stronger, the double-mode oscillation disappears, whereas a localized oscillation mode emerges. Furthermore, we investigate a propagating wave phenomenon and a localized mode observed in the six inductor-coupled hard-oscillator rings. We show that the propagating wave corresponds to a multimode oscillation with several dominant peaks in a spectral distribution, and that the solution originates in the neighbourhood of a local bifurcation point of the localized mode.

Chapter Contents:

• 7.1 Introduction
• 7.2 Two inductor-coupled hard oscillators
• 7.2.1 Weakly nonlinear oscillators
• 7.2.1.1 Averaged equation
• 7.2.1.2 Averaged equation of two coupled hard oscillators
• 7.2.1.3 Double-mode oscillation in two coupled hard oscillators
• 7.2.2 Strongly nonlinear oscillators
• 7.3 Propagating waves in a coupled hard-oscillator ring
• 7.4 Conclusions
• References

Inspec keywords: inductors; relaxation oscillators

Other keywords: spectral distribution; double-mode oscillation; higher-order nonlinearity; multimode oscillations; Van der Pol oscillators; local bifurcation point; propagating wave phenomenon; localized oscillation modes; inductor-coupled hard-oscillator rings; weakly nonlinear oscillators

Subjects: Oscillators