Rotations in both poloidal and toroidal directions of a tokamak edge plasma have important interactions with various other plasma phenomena including plasma stability and transport. Solutions for rotation velocities were studied, using differential equations comprising the ambipolarity constraint and the parallel momentum balance equations of the revisited neoclassical theory, with the corrected contribution also from the gyro-viscosity tensor. Temperature and density profiles with realistic pedestal forms were considered given and controlled parametrically. The similarity of this equation system to reaction-diffusion equations was utilized in the numerical simulation and the study of critical points on the bifurcation diagrams. It was found that the steepness of the density and temperature gradients has important effects on the rotation stability and on its bifurcative behaviour.