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Stability of the Toda equations related to a perturbed $R_i$ type recurrence relation

Stability of the Toda equations related to a perturbed $R_i$ type recurrence relation

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 …