chaos in the system is to calculate the largest Lyapunov exponent. (In our reduced two-dimensional phase space since the flow is Hamiltonian, the Lyapunov exponents come in pairs of opposite sign.) Because our phase-space is bounded, we use a slightly modified approach from that used for an unbounded system to the calculation of the exponent, as outlined in Reichl[@reichl]. The (largest) Lyapunov exponent is defined by, $$\label{eq:eq17}
\lambda_n(\tau,{\rm{\bf X}}_{0,0},{\rm{\bf Y}}_{0,0}) = 
\frac{1}{n\tau}
\sum_{j=1}^{n} \ln\left(\frac{d_j}{d_0}\right),$$ where $d_0 = |{\rm{\bf Y}}_{0,0}~-~{\rm{\bf X}}_{0,0}|$ is the Euclidean distance between the position of neighboring trajectories labelled by [**X**]{}$_{0,0}$ and [**Y**]{}$_{0,0}$, and $\{d_j\}, j=1,\dots,n$ are the sequence of distances generated between the trajectories at $n$ successive time steps. If $d_0$ is not too big, then the limit, $lim_{n\uparrow\infty} 
\lambda_n(\tau,{\rm{\bf X}}_{0,0},{\rm{\bf Y}}_{0,0}) = 
\lambda({\rm{\bf X}}_{0,0})$ exists, and is independent of both $d_0$ and $\tau$. Furthermore, $\lambda({\rm{\bf X}}_{0,0})$ is zero if [**X**]{}$_{0,0}$ is chosen in a regular region, while it is positive if [**X**]{}$_{0,0}$ is chosen to lie in a chaotic region.

With the help of the Lyapunov exponent we constructed the ‘phase diagram’ shown in Fig.1 for this system in the $(\epsilon,{\tilde\omega_c})$ parameter space in the following fashion. For a given set of parameters $(\epsilon,{\tilde\omega_c})$, we choose 