  In this article we construct the parameter region where the existence of a
homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like
system will be analytically proved in the case of a nonnegative saddle value.
Then, for a qualitative description of the different types of homoclinic
bifurcations, a numerical analysis of the detected parameter region is carried
out to discover several new interesting bifurcation scenarios.
