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We study reaction dynamics on a model potential energy surface exhibiting post-transition state bifurcation in the vicinity of a valley ridge inflection (VRI) point. We compute fractional yields of products reached after the VRI region is traversed, both with and without dissipation. It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics. Moreover, when dissipative effects are incorporated, the product ratio depends in a complicated and highly non-monotonic fashion on the dissipation parameter. Dynamics in the vicinity of the VRI point itself play essentially no role in determining the product ratio, except in the highly dissipative regime.