DYNAMICAL ANALYSIS OF TWO LOAN CATEGORIES IN A BANKING SYSTEM WITH NON-PERFORMING LOANS

Abstract

The ability of banks to extend credit and meet their obligations to depositors can be significantly affected by the presence of non-performing loans (NPL). The intermediation process, in which deposits are transformed into loans, can be represented through a predator–prey modeling framework. In this study, we formulate and analyze a system of three nonlinear ordinary differential equations representing deposits as the prey and two categories of loans, individual loans and company loans, as predators within a single banking system. The model incorporates the effect of NPLs as factors that reduce effective loan performance and influence system interactions. The analytical results show that the system possesses five equilibrium points. The equilibrium corresponding to the absence of deposits and loans is unstable, while the remaining four equilibria are globally asymptotically stable under specific parameter conditions, particularly those related to loan growth rates and NPL levels. The stability analysis indicates that higher NPL rates tend to reduce the stability region of equilibria and may destabilize the banking system. Furthermore, numerical simulations are conducted to support and illustrate the analytical findings. These results provide insight into the long-term dynamic behavior of deposits and loans, emphasizing the role of NPLs in determining banking system stability.