  We study the collective dynamics of a two-dimensional honeycomb lattice of
magnetic skyrmions. By performing large-scale micromagnetic simulations, we
find multiple chiral and non-chiral edge modes of skyrmion oscillations in the
lattice. The non-chiral edge states are due to the Tamm-Shockley mechanism,
while the chiral ones are topologically protected against structure defects and
hold different handednesses depending on the mode frequency. To interpret the
emerging multiband nature of the chiral edge states, we generalize the massless
Thiele's equation by including a second-order inertial term of skyrmion mass as
well as a third-order non-Newtonian gyroscopic term, which allows us to model
the band structure of skrymion oscillations. Theoretical results compare well
with numerical simulations. Our findings uncover the importance of high order
effects in strongly coupled skyrmions and are helpful for designing novel
topological devices.
