(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Non-performing loan (NPL) and deposit withdrawal are two factors that can affect loan and deposit volumes in the bank. The distribution of deposits into loans at banks can be modelled using the predator-prey model. In this research, we proposed and analysed a mathematical model dealing with two loans, i.e. a loan for individuals and a loan for companies, at one bank, which is developed from two predators and one prey model. We aim to study the dynamics and its long-term behaviour of the proposed model, as well as to discuss the effects of the NPL and deposit withdrawal parameters associated with the model. The results of the analysis shows that the model has five equilibrium points, namely the equilibrium points without deposit and loan activities, the loan-free equilibrium point, the individual’s loan-free equilibrium point, the company’s loan-free equilibrium point, and the equilibrium point with deposit and loan activities. It is found that the equilibrium point without deposit and loan activities in the bank is always unstable, while the other equilibrium points are globally asymptotically stable if their certain conditions are satisfied. The theoretical results are verified by our numerical simulations.