  In this manuscript, a modified $R_I$ type recurrence relation is considered
whose recurrence coefficients are perturbed by addition or multiplication of a
constant. The perturbed system of recurrence coefficients is represented by
Toda lattice equations, which are derived. These equations are then represented
in a matrix form. With the help of this matrix representation, a known Lax pair
is recovered. Inferences about the stability of resulting perturbed system of
Toda equations are drawn based on numerical experiments.
