  Using numerical simulations of an extended Lugiato-Lefever equation, we
analyze the stability and nonlinear dynamics of Kerr frequency combs generated
in microresonators and fiber resonators taking into account third-order
dispersion effects. We show that cavity solitons underlying Kerr frequency
combs, normally sensitive to oscillatory and chaotic instabilities, are
stabilized in a wide range of parameter space by third-order dispersion.
Moreover, we demonstrate how the snaking structure organizing compound states
of multiple cavity solitons is qualitatively changed by third-order dispersion,
promoting an increased stability of Kerr combs underlined by a single cavity
soliton.
