  We numerically investigated the quantum-classical transition in rf-SQUID
systems coupled to a dissipative environment. It is found that chaos emerges
and the degree of chaos, the maximal Lyapunov exponent $\lambda_{m}$, exhibits
non-monotonic behavior as a function of the coupling strength $D$. By measuring
the proximity of quantum and classical evolution with the uncertainty of
dynamics, we show that the uncertainty is a monotonic function of $\lambda
_{m}/D$. In addition, the scaling holds in SQUID systems to a relatively
smaller $\hbar_{eff}$, suggesting the universality for this scaling.
