<![CDATA[This study develops a three-dimensional nonlinear ordinary differential-equation model linking normalized deposits, loans, and liquidity through liquidity-dependent deposit pressure. The analysis derives the equilibrium conditions while retaining the regularization parameter, examines conditional positivity and boundedness, and evaluates local stability using the Jacobian and Routh–Hurwitz criterion. The nonnegative orthant is not generally forward invariant; therefore, global positivity is not claimed. For a literature-informed illustrative baseline, the model admits two positive interior equilibria. The lower equilibrium (D=0.165214, L=0.141010, R=0.047210) is unstable, whereas the upper equilibrium (D=0.999790, L=0.853321, R=0.285690) is locally asymptotically stable. The origin is also locally stable in the mathematical domain. Recalculated fourth-order Runge–Kutta simulations and ±5% one-at-a-time sensitivities show how the 50-year normalized indices respond to baseline parameters; deposit carrying capacity has the largest positive local sensitivity for deposits under the selected conditions. The numerical parameters are assumed or literature-informed rather than fitted to historical banking observations. Accordingly, the model offers a conditional theoretical account of nonlinear banking feedback and requires formal parameter estimation and external validation before operational or regulatory application.]]>
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