Study on a hyper-chaotic financial system with synchronization

The nonlinear financial system can describe the hyper-chaotic behaviour of global stock markets, inflation in an economy, share market downturns, exchange rate fluctuation, and other highly complex and interconnected phenomena of an economy. This paper presents a four-dimensional hyperchaotic financial system incorporating the exchange rate as a new factor alongside interest rate, investment demand, and price index. The instability arising from exchange rate fluctuations poses significant challenges to financial stability and market dynamics. To address this, equilibrium points, stability conditions, dissipative properties, bifurcation patterns, and Lyapunov exponents are analysed, confirming hyperchaotic behaviour. To stabilize the system, global exponential synchronization and asymptotic synchronization controllers are proposed. Their effectiveness in suppressing chaos and restoring stability is validated through mathematical proofs and numerical simulations, demonstrating their potential for financial policy application.