  Aims. We carry out the self-consistent dynamic evolution of the orbital
structure of Milky Way globular clusters. This allows us to estimate possible
and probable close passages and even collisions of the clusters with each
other. Methods. We reproduced the orbits of 147 globular clusters in 10 Gyr
lookback time using our own high-order N-body parallel dynamic phi-GPU code.
The initial conditions (three coordinates and three velocities for the present
time) were derived from the Gaia DR3 catalogue. The galaxy is represented by
five external potentials from the IllustrisTNG-100, whose masses and sizes of
the disk and halo components are similar to the physical values of the Milky
Way at present. Results. We present a statistical analysis of the cumulative
close passages rate: About ten close passages with relative distances shorter
than 50 pc for every billion years for each of the five external potentials. We
present the 22 most reliable collision pairs with a good probability. As an
example: Terzan 4 versus Terzan 2 (49%), Terzan 4 versus NGC 6624 (44%), Terzan
4 versus Terzan 5 (40%), Terzan 4 versus NGC 6440 (40%), and Terzan 4 versus
Liller 1 (42%). The most active globular cluster in the collision sense is
Terzan 4, which has 5.65 collision events on average (averaged over all
individual 1000 initial condition realisations). Most collisions are located
inside the Galactic disk and form two ring-like structures. The first ring-like
structure has the highest collision number density at 1 kpc, and the second
sturcture has a maximum at 2 kpc. Conclusions. Based on our numerical
simulations, we can conclude that the few dozen Milky Way globular clusters
probably undergo some close encounters and even possible collisions during
their lifetimes, which can significantly affect their individual dynamical
evolution and possibly even their stellar content.
