  In the present article we carry out a molecular dynamics study of the
core-softened system and show that the existence of the water-like anomalies in
this system depends on the trajectory in $P-\rho-T$ space along which the
behavior of the system is studied. For example, diffusion and structural
anomalies are visible along isotherms, but disappears along the isochores and
isobars, while density anomaly exists along isochors. We analyze the
applicability of the Rosenfeld entropy scaling relations to this system in the
regions with the water-like anomalies. It is shown that the validity of the of
Rosenfeld scaling relation for the diffusion coefficient also depends on the
trajectory in the $P-\rho-T$ space along which the kinetic coefficients and the
excess entropy are calculated.
