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In this study, a nonlinear dynamical system is developed to analyze the dynamics of Indian exports to USA, the US tariff rate on Indian goods, and the competitiveness of India’s export sector. The model is formulated as a three-dimensional system of differential equations that incorporates logistic growth in exports, tariff adjustments driven by trade imbalances, and the evolution of competitiveness shaped by innovation, productivity, and global demand. Each equation reflects a distinct economic mechanism: nonlinear export growth under capacity constraints, tariffs as feedback responses, and competitiveness as an adaptive dynamic. Analytical investigation reveals the existence of an interior equilibrium and provides conditions for its local asymptotic stability using the Routh–Hurwitz criterion. The resulting stability condition is used to derive a parameter-dependent stability region in the competitiveness–tariff space. Phase portraits and contour plots illustrate the system’s dynamic behavior under various policy scenarios. Numerical simulations further reveal threshold effects in export sustainability and identify parameter regions where small tariff adjustments destabilize trade flows. The findings underscore critical policy implications, suggesting that adaptive tariff strategies and sustained competitiveness are essential for maintaining India’s trade stability under evolving US tariff regimes.