Synchronization of 4D Hyperchaotic Economic Systems via Barrier Function Based Control Technique

This paper analyzes the nonlinear dynamics and synchronization characteristics of a four-dimensional hyperchaotic model for macro-financial systems based on financing tension, investment demand, production cost, and profit margin. Using techniques like Lyapunov exponents, Kaplan–Yorke dimension, bifurcation analysis, Poincaré sections, permutation entropy, and the 0–1 test for chaos, a thorough method of evaluating chaos is used. These techniques aid in determining the intrinsic complexity of the model and confirm the existence of hyperchaotic behaviour, which expands in multiple directions in the phase space. Regardless of initial conditions, a global synchronization technique is developed that guarantees stability within a predetermined time frame. This method manages high-dimensional instability under realistic safety standards using a logarithmic barrier Lyapunov function and predefined performance functions. The controller ensures that synchronization errors stay within predetermined bounds that fluctuate over time and reach zero within a given time frame. This method's stability is verified by a thorough Lyapunov analysis, and analytical techniques also demonstrate its ability to resist to bounded external disturbances.A sample macro-financial stress scenario using consolidated industrial financial indicators is included to demonstrate practical relevance. This makes it possible to examine the consistency between observed economic fluctuations and simulated nonlinear volatility qualitatively. The suggested control framework's robustness, strict constraint compliance, and quick convergence are confirmed by numerical simulations.The results provide a mathematically supported method for limited stabilization of hyperchaotic macrofinancial dynamics as well as a systematic approach for risk containment and performance guaranteed synchronization in complex nonlinear economic systems.