  We show by micromagnetic simulations that spontaneous skyrmion ground state
can exist in Co/Ru/Co nanodisks without the Dzyaloshinsky-Moriya interaction
(DMI), which can remain stable in the applied magnetic field along +z direction
even up to 0.44 T. The guiding center ($R_x$,$R_y$) of skyrmion defined by the
moments of the topological density presents a novel gyration with a star-like
trajectory in a pulsed magnetic field and a hexagonal trajectory after the
field is switched off, which is different from that of vortex or bubble. One of
the coupled skyrmions could move without an external magnetic field, but only
induced by the motion of the other one due to strong inter-layer magnetostatic
interactions. This work sheds light on how novel skyrmions can be discovered in
various (not limited to magnetic) systems with competing energies and
contributes to the understanding of the dynamical properties of skyrmion.
