  We study orbital evolution of multi-planet systems that form a resonant
chain, with nearest neighbours close to first order commensurabilities,
incorporating orbital circularisation produced by tidal interaction with the
central star. We develop a semi-analytic model applicable when the relative
proximities to commensurability, though small, are large compared to
epsilon^(2/3) , with epsilon being a measure of the characteristic planet to
central star mass ratio. This enables determination of forced eccentricities as
well as which resonant angles enter libration. When there are no active linked
three body Laplace resonances, the rate of evolution of the semi-major axes may
also be determined. We perform numerical simulations of the HD 158259 and EPIC
245950175 systems finding that the semi-analytic approach works well in the
former case but not so well in the latter case on account of the effects of
three active three body Laplace resonances which persist during the evolution.
For both systems we estimate that if the tidal parameter, Q', significantly
exceeds 1000, tidal effects are unlikely to have influenced period ratios
significantly since formation. On the other hand if Q' < ~ 100 tidal effects
may have produced significant changes including the formation of three body
Laplace resonances in the case of the EPIC 245950175 system.
