<![CDATA[This study examines the joint evolution of conventional and Islamic banking assets in Indonesia using a non-autonomous Lotka–Volterra competition model. The model was calibrated to a compiled annual series for 2016–2024 with time-dependent intrinsic growth and capacity terms, constrained nonlinear least squares, and adaptive Runge–Kutta integration. The working series includes two interpolated observations (2017–2018). For these inputs, the time-dependent model achieved in-sample MAPE of 1.52% for Islamic banking and 2.22% for conventional banking, while the fitted interaction coefficients were near zero under the imposed bounds. Nevertheless, the constant-parameter model had the lowest reported AICc, and five rolling-origin tests produced mean errors of 7.69% and 5.50%, respectively. Bootstrap and enlarged-bound analyses indicated weak identification of several growth and capacity parameters. Frozen-time Jacobian calculations yielded locally stable equilibria for the autonomous systems evaluated at the observed years, without establishing stability of the full non-autonomous system. A continuation to 2028 produced a conditional Islamic-market-share median near 7.2% and a reported 90% bootstrap interval of 6.4–9.2%. These outputs describe the behavior of the retained dataset and model assumptions rather than a causal effect of the 2021 BSI merger or a validated financial forecast. The results underscore the importance of complexity penalties, identifiability analysis, and source-data provenance in aggregate financial-dynamics modeling.]]>
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