Bifurcation analysis on Dynamic model of Bank's Loan and Deposit Volume

Abstract

This thesis develops and analyzes a nonlinear continuous-time dynamical system describing the interaction between bank deposits D(t) and outstanding loans L(t) in the intermediation process. Building on a baseline interaction structure, the thesis proposes a sequence of extended models to better reflect operational constraints and prudential policy channels. Model 3, as developed in previous studies, introduces required reserves through the reserve ratio m, which reduces effective lendable deposits and alters the system’s equilibrium and stability properties. On this foundation, Model 4 is proposed as a new and improved specification of Model 3 by incorporating a capacity-utilization mechanism through the normalization term D k in the intermediation channel, together with bounded deposit dynamics (logistic carrying capacity k) and saturation effects in the deposit-to-loan transformation. Methodologically, the thesis derives feasible equilibria, studies local stability via Jacobian linearization and trace–determinant conditions, and investigates regime changes through bifurcation analysis with the maximum mixing rate p as the primary control parameter. The results identify critical thresholds of p governing the existence and stability of the positive coexistence equilibrium. Numerical simulations use interest rate of Vietnamese bank market in Q3- 2025 to illustrate the model’s dynamic behavior. Comparative evidence indicates that Model 4, through the capacity-utilization term D k , yields a wider and more interpretable stability region in p than Model 3, while highlighting how reserve requirements shift stability boundaries and affect the implied loan-to-deposit ratio (LDR). Overall, the thesis provides a tractable qualitative framework for prudential discussions of deposit–loan dynamics and motivates econometric validation as a natural next step.