Hopf Bifurcation and new singular orbits coined in a Lorenz-like system

We seize some new dynamics of a Lorenz-like system: $dot{x} = a(y - x)$, quad $dot{y} = dy - xz$, quad $dot{z} = - bz + fx^{2} + gxy$, such as for the Hopf bifurcation, the behavior of non-isolated equilibria, the existence of singularly degenerate heteroclinic cycles and homoclinic and heteroclinic orbits. In particular, our new discovery is that the system has also two heteroclinic orbits for $bg = 2a(f + g)$ and $a > d > 0$ other than known $bg > 2a(f + g)$ and $a > d > 0$, whose proof is completely different from known case. All the theoretical results obtained are also verified by numerical simulations.