  The stochastic logistic model with regime switching is an important model in
the ecosystem. While analytic solution to this model is positive, current
numerical methods are unable to preserve such boundaries in the approximation.
So, proposing appropriate numerical method for solving this model which
preserves positivity and dynamical behaviors of the model's solution is very
important. In this paper, we present a positivity preserving truncated
Euler-Maruyama scheme for this model, which taking advantages of being explicit
and easily implementable. Without additional restriction conditions, strong
convergence of the numerical algorithm is studied, and 1/2 order convergence
rate is obtained. In the particular case of this model without switching the
first order strong convergence rate is obtained. Furthermore, the approximation
of long-time dynamical properties is realized, including the stochastic
permanence, extinctive and stability in distribution. Some simulations and
examples are provided to confirm the theoretical results and demonstrate the
validity of the approach.
