Bifurcation analysis of a non linear 6D financial system with three time delay feedback

Nonlinear financial systems capture real-world economic and financial complexities, enabling deeper insights into stock market crashes, feedback mechanisms, currency devaluations, and emergent behaviors. The purpose of this study is to investigate the structure of a nonlinear financial system that incorporates interest rates, investment demand, price index, GDP growth rate, unemployment rate, and vacancy availability rate into the system. Time delays in financial systems describe the time gap between economic decisions and real-life implementations. In this study, three different time delays are incorporated in investment demand, GDP growth, and vacancy creation. We consider four cases to describe the intrinsic dynamics of economic factors. First, we consider the system without time delays, and branch point bifurcation, transcritical bifurcation, and Hopf bifurcation for different parameters, such as government debt, novice entrepreneurs, and capital stock, are investigated. Secondly, this research highlights the sensitivity of the financial system to the delay in vacancy creation, and it has been noted that when the delay in vacancy formation increases, it becomes more challenging for the six state variables to be stable. Next, we consider the time delay in GDP and investigate the stability of the system for the time lag. Lastly, we consider all three time delays, and the financial system switches its stability when the delays attain their critical values. The research demonstrates, through advanced computer simulations, how financial systems may be altered by a change in policy or by an external force or market fluctuations.