  We study effects of the particles coupling with scalar field (SF) on the
distribution of stable circular orbits (SCO) around the naked singularity
described by the well-known Fisher-Janis-Newman-Winicour solution. The
power-law and exponential models of the particle--SF interaction are analyzed.
The focus is on the non-connected SCO distributions. We show that coupling
between particles and SF can essentially complicate the topology of the SCO
distributions. In particular, it can lead to new non-overlapping SCO regions,
which are separated by unstable orbits and/or by regions where the circular
orbits do not exist.
