The problem of analyzing the internal mechanisms of structural transformations of non-equilibrium regimes in multi-component biological systems with random fluctuations is considered. Based on the Li–Rinzel model, we study how parametric noise deforms calcium oscillations, which play a key role in cellular processes. The conditions under which random forcing generates or suppresses spiking calcium oscillations are discussed. Parametric analysis of such stochastic transformations of calcium relaxation self-oscillations is carried out using statistics extracted from direct modeling and a new theoretical approach based on the method of confidence domains. © 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.