  The long-standing co-orbital asteroids have been thought to be the possible
source of zodiacal dust ring around the orbit of Venus, but inconsistent
conclusions on the orbital stability thus existence of Venus Trojans are found
in literature. We present in this paper a systematic survey of the orbital
stability of Venus Trojans, taking into account the dynamical influences from
the general relativity and the Yarkovsky effect. The orbits of thousands of
fictitious Venus Trojans are numerically simulated. Using the method of
frequency analysis, their orbital stabilities and the dynamical mechanisms
behind are described in detail. The influences of general relativity and of
Yarkovsky effect, which were either neglected or oversimplified previously, are
investigated by long-term numerical simulations. The stability maps on the
$(a_0,i_0)$ plane and $(a_0,e_0)$ plane are depicted, and the most stable Venus
Trojans are found to occupy the low-inclination horseshoe orbits with low
eccentricities. The resonances that carve the fine structures in the stability
map are determined. The general relativity decreases the stability of orbits by
little but the Yarkovsky effect may drive nearly all Venus Trojans out of the
Trojan region in a relatively short time. The Venus Trojans have poor orbital
stability and cannot survive the age of the Solar system. The zodiacal dust
ring found around the orbit of Venus is more likely a sporadic phenomenon, as
the result of temporarily capture into the 1:1 mean motion resonance of dust
particles produced probably from passing comets or asteroids, but not Venus
Trojans.
