Resonance beyond mechanics: from Kazimieras Ragulskis’ Vibroengineering school to financial saturation theory

This paper examines the methodological relationship between the Vibroengineering School founded and scientifically led by Academician Kazimieras Ragulskis and Financial Saturation Theory (FST). Rather than transferring mechanical laws directly into economics, the study identifies structural parallels in nonlinear systems: nonlinearity, feedback, self-excitation, synchronization, resonance, and transitions between stable and unstable regimes. FST addresses a different class of systems but proposes a comparable qualitative mechanism: increasing saturation raises interaction density, strengthens feedback, and may generate synergy, self-synchronization, economic resonance, bifurcation, and financial instability. The paper adds a mathematical comparison of critical amplification based on the two response curves shown in Fig. 1. The saturation-productivity function and the normalized resonance-response function both exhibit square-root divergence as their respective normalized variables approach the critical boundary. Their leading critical exponent is therefore the same, although their coefficients, variables, and underlying mechanisms differ. This establishes an asymptotic structural correspondence, not dynamical isomorphism. The result refines the proposed methodological bridge and defines explicit limits on cross-disciplinary transfer. FST is presented as one possible interdisciplinary expression of a broader tradition of nonlinear systems thinking.