ANALYSIS OF BANKING DEPOSIT COST IN THE DYNAMICS OF LOAN: BIFURCATION AND CHAOS PERSPECTIVES

Ansori, Moch. Fandi
Hariyanto, Susilo

BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 16 No 4 (2022): BAREKENG: Journal of Mathematics and Its Applications

A dynamic model of banking loan based on the gradient adjustment process is presented. The amount of loan that will be channeled in the future depends on the sign of the marginal profit of loan. In this paper, we study the deposit cost in the dynamics of a bank’s loan using bifurcation theory. The analysis shows that the deposit cost can affect the stability of loan equilibrium. If the deposit cost is too high, then the loan equilibrium can lose its stability trough transcritical bifurcation. Meanwhile, if the deposit cost is too low, then the loan equilibrium may lose its stability via flip bifurcation and road to chaos. The loan equilibrium stable if the deposit cost is in between the bifurcation values. These findings are confirmed by the numerical simulations. In addition, we present the graph of Lyapunov exponent to see the existence of chaos and the graph of chaotic loan that is sensitive to the initial condition.