The nonlinear dynamics of a spherical gas bubble in a liquid water is reconsidered on the basis of the Rayleigh-Plesset equation with particularly emphasis on the unstable behavior with respect to infinitesimal perturbations. The evolution of bubble radius after the discontinuous change of ambient pressure is theoretically analyzed, and the classical critical pressure and critical radius are re-derived as a saddle-node bifurcation point, when the center and saddle on the phase plane merge into a degenerate unstable singular point in the phase plane. Before the saddle-node bifurcation, there is a separatrix issuing from and entering into the saddle point in the inviscid limit. We propose a new criterion for cavitation inception: the ambient pressure that makes the separatrix pass through the initial bubble radius. This criterion gives a cavitation inception pressure higher than the classical one. The effects of viscosity and thermal conductivity are also discussed.

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