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We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat FLRW background. We consider cosmological models with non-minimally coupled scalar fields and polynomial potentials. In particular, the model that contains the Hilbert-Einstein curvature term, the conformal coupling term and the Higgs-like potential with an opposite sign is studied in detail. Bounce solutions with non-monotonic Hubble parameters have been found and analysed. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant. My talk is particularly based on the paper by E.O. Pozdeeva, M.A. Skugoreva, A.V. Toporensky, S.Yu. Vernov, JCAP 1612 (2016) no.12, 006 [arXiv:1608.08214]