Figure 3

The energy level lines${\mathbf{\Gamma }}^{{\mathit{\ell }}_{\mathbf{0}}}$,${\mathbf{\Gamma }}^{{\mathit{\ell }}_{\mathbf{1}}}$and${\mathbf{\Gamma }}^{{\mathit{\ell }}^{\mathbf{\ast }}}$for system (2.7) superimposed over the stable and unstable manifolds of${\mathit{P}}_{\mathbf{\pm }}$for system (2.7). The colored regions are the invariant sets ℰ (the darker one) and ℱ (lighter). The figure has been plotted with the parameters $k=1$, ${\mu }_0=1/2$, ${\mu }_1=2$. For graphical reasons, a slightly different x- and y-scaling has been used.