Dynamics of Deposit and Loan Volumes Model with Non-Performing Loan and Deposit Withdrawal Factors

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 propose and analyse 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 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 show that the model has five equilibrium points. We find 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.