$R_{0}$ has a fix value, chosen for consistency with previous papers [@burgio-95; @baldo-96; @baldo-98; @felea-09a] as $6\ \rm{fm}$.

A Runge-Kutta type algorithm (order 2-3) with an optimized step size was used for solving the system of differential equations, while keeping the absolute errors for the phase space variables under $10^{-6}$ and conserving the total energy with relative error: $\Delta E/E \approx 10^{-8}$ (Fig. \[fig:1\]).

We imposed the equilibrium condition between the pressure exerted by the particles and the mechanical pressure of the wall [@burgio-95; @baldo-96; @baldo-98; @felea-09a] and thus obtained for the initial equilibrium value of the collective variable, perturbed with a small value:

$$\alpha_{0}=\frac{-1+\sqrt{1+8T/{mR_0^2\Omega ^2}}}{2}+0.15,$$

where $T=36\ \rm{MeV}$ [@burgio-95; @baldo-96; @baldo-98; @felea-09a] is the two-dimensional kinetic energy and also the temperature of the nuclear system, when considering the natural system of units ($\hbar=c=k_{B}=1$).

\[sec:2\]The quantitative analysis of the route to chaos
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We carry on the study begun in [@felea-09a] by gradually changing the degree of vibration of the potential wall from a slow motion (adiabatic state) to a rapid one (the so-called resonance state of the interaction). In the first case, the collective motion is described by a radian frequency smaller than $0.05\ c/\rm{fm}$. The latter is dominated 