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We investigate FRW cosmological solutions in the theory of modulus fieldcoupled to gravity through a Gauss-Bonnet term. The explicit analytical formsof nonsingular asymptotics are presented for power-law and exponentially steepmodulus coupling functions. We study the influence of modulus field potentialon these asymptotical regimes and find some forms of the potential which do notdestroy the nonsingular behavior. In particular, we obtain that exponentiallysteep coupling functions arising from the string theory do not allownonsingular past asymptotic unless modulus field potential tends to zero formodulus field $\psi \to \pm \infty$. Finally, the modification of the chaoticdynamics in the closed FRW universe due to presence of the Gauss-Bonnet term isdiscussed.Comment: 14 pages, 3 Postscript figures, uses epsf.st

Non-singular cosmological models in string gravity with constant dilaton and second-order curvature corrections