Stability of oscillations

We must also examine the stability of the periodic solution and its limit cycle as it emerges from the bifurcation point. Just as stationary states may be stable or unstable, so may oscillatory solutions. If they are stable they may be observable in practice if they are unstable they will not be directly observable although their existence still has some physical relevance. We will give the recipe for evaluating the stability and character of a Hopf bifurcation in the 

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When a quartz resonator is in contact with a viscous liquid, viscous coupling is operative (Figure 2-(b)). The added effect of viscous liquid modifies the equivalent circuit to include both the mass loading density component (Ll), and a resistive viscosity component (RJ of the liquid. The increase of the total value of the resistor (Ri + RJ, results in reducing the radii in admittance circles, which affects the stability of oscillation. The series resonance frequency shifts its value when a QCM is immersed in the liquid. The new resonance frequency due to the increased inductance from the viscous liquid is,... 

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