Credit and deposit dynamics with external capital in a logistic model

In banking, the provision of credit does not only depend on customer deposit funds but also on external funding sources. A system of differential equations is formulated to describe the interaction between lending and deposits, incorporating external funding as a parameter influencing the credit supply. The model introduces external funding sources to enhance the maximum sustainable lending capacity of the bank. Local equilibrium analysis with eigenvalue-based determination states that when banks rely solely on external funds for lending, banks are unstable under disturbances, but bank lending will be stable if bank used external funds and deposits for lending. The model is validated using ten years of commercial banking data, with parameter estimation via PSO with inertia parameter yielding a 1.7% MAPE for deposit model and 2.008% MAPE for loan model in replicating observed deposit-loan dynamics.