A problem of the study of underlying mechanisms for structural transformations in coupled multicomponent biological systems is considered. We focus on the case of two coupled subunits, which, being isolated, exhibit chaotic modes. We use the Hassell map as a conceptual model for subunits. A variety of non-equilibrium mono- and multistable oscillatory regimes with in-phase and anti-phase synchronization in the coupled system is described. An impact of random disturbances on the these regimes is studied. High sensitivity to noise causing stochastic transformations from anti-phase to in-phase synchronization is investigated. We show how such transformations of the synchronization modes are accompanied by transitions from order to chaos.