  In this work, we conduct a rigorous analysis on the dynamics of a
predator-prey model with cooperative predation. From the root classification of
an algebraic equation, we derive existence criteria of the positive equilibria.
By Jacobian matrix and central manifold theory, we find critical conditions
under which the positive equilibria are locally asymptotically stable or
unstable. We also use a careful computation to obtain a concise and explicit
formula for the first Lyapunov coefficient. Especially, we prove that the Hopf
bifurcation induced by the cooperative predation is always supercritical, which
means that the sustained oscillations near the Hopf bifurcation points are
locally asymptotically stable.
