  Proxima Centauri was recently discovered to host an Earth-mass planet of
Proxima b, and a 215-day signal which is probably a potential planet c. In this
work, we investigate the dynamical evolution of the Proxima Centauri system
with the full equations of motion and semi-analytical models including
relativistic and tidal effects. We adopt the modified Lagrange-Laplace secular
equations to study the evolution of eccentricity of Proxima b, and find that
the outcomes are consistent with those from the numerical simulations. The
simulations show that relativistic effects have an influence on the evolution
of eccentricities of planetary orbits, whereas tidal effects primarily affects
the eccentricity of Proxima b over long timescale. Moreover, using the MEGNO
(the Mean Exponential Growth factor of Nearby Orbits) technique, we place
dynamical constraints on orbital parameters that result in stable or
quasi-periodic motions for coplanar and non-coplanar configurations. In the
coplanar case, we find that the orbit of Proxima b is stable for the semi-major
axis ranging from 0.02 au to 0.1 au and the eccentricity being less than 0.4.
This is where the best-fitting parameters for Proxima b exactly fall.
Additional simulations show that the robust stability of this system would
favor an eccentricity of Proxima b less than 0.45 and that of Proxima c below
0.65. In the non-coplanar case, we find that mutual inclinations of two planets
must be lower than $50^{\circ}$ in order to provide stability. Finally, we
estimate the mass of Proxima c to be $3.13~{M_ \oplus } \le {m_c} \le 70.7~{M_
\oplus }$ when $1.27~{M_ \oplus } \le {m_b} \le 1.6~{M_ \oplus }$, if
${i_{mutual}} \le {50^{\circ}}$ and $\Delta \Omega = 0^{\circ}$.
