Hopf bifurcation of a financial dynamical system with delay

TL;DR

This paper analyzes a delayed financial dynamical system, demonstrating that it undergoes a Hopf bifurcation, with stability analysis and numerical simulations revealing the system's dynamic behavior and oscillatory patterns.

Contribution

It introduces a delayed financial model and provides a detailed stability and bifurcation analysis, highlighting the occurrence of Hopf bifurcation in such systems.

Findings

System undergoes Hopf bifurcation

Stability analysis confirms bifurcation points

Numerical simulations illustrate oscillatory dynamics

Abstract

The aim of this work is to investigate the qualitative behaviour of a financial dynamical system which contains a time delay. We investigate the dynamic response of this system of which variables are interest rate, investment demand, price index and average profit margin. We perform a stability analysis at the fixed points and show that the system undergoes a Hopf bifurcation. The bifurcation analyses are supported by numerical simulations.