A classical nonlinear system, the "Brusselator", was used to illustrate the modeling and simulation of oscillating chemical systems using stability analysis techniques with modern software tools such as Comsol Multiphysics, Matlab, and Excel. A systematic approach is proposed in order to establish a regime of parametric conditions that lead to oscillations in chemical systems. A Matlab script that symbolically finds the equilibrium points of the system, and the Jacobian of the assembly matrix at equilibrium was written. The Matlab script also calculates the trace, determinant and discriminant of the Jacobian and finds the critical points for which the trace and determinant are zero. An emphasis on finding the bifurcation points is made in the simulations and on the conditions for the onset of limit cycles, which are of most interest in biological systems.