Chaotic systems are known to be extremely sensitive to initial conditions, meaning small changes can have a significant impact on the outcomes. By analyzing the average profit margin in relation to chaotic dynamics, companies can conduct sensitivity analysis to assess the potential impact of various factors on their profitability. This analysis can help identify critical variables or scenarios that may significantly affect profit margins. In this article, we have proposed a hyperchaotic financial system with sinusoidal hyperbolic non-linear variables applied to the average profit margin. Furthermore, we have investigated the stability of the hyperchaotic financial dynamics model to provide information to companies to assess the consistency and reliability of their profitability. In addition, fundamental dynamic behavior like Lyapunov exponents, bifurcation analysis, coexisting attractors have been reported. Finally, a nonlinear feedback control approach is developed to train an adaptive neural fuzzy controller. The application of Lyapunov theory confirms that this nonlinear feedback controller can effectively minimize the synchronization error within a finite duration. The results from simulations establish the effectiveness of the proposed neural fuzzy controller architecture in controlling the synchronization of two hyperchaotic financial models. Additionally, the simulation includes a comparison between the performance of the nonlinear controller and the adaptive neural fuzzy controller.

Supply chains comprise various interconnected components like suppliers, manufacturers, distributors, retailers, and customers, each with unique variables and interactions. Managing dynamic supply chains is highly challenging, particularly when considering various sources of risk factors. This paper extensively explores dynamical analysis and multistability analysis to understand nonlinear behaviors and pinpoint potential risks within supply chains. Different phase portraits are used to demonstrate the impact of various factors such as transportation risk, quality risk, distortion, contingency reserves, and safety stock on both customers and retailers. We introduced a sliding mode control method that computes the sliding surface and its derivative by considering the error and its derivative. The equivalent control law based on the sliding surface and its derivative is derived and validated for control purposes. Our results show that the controller SMC can significantly enhance supply chain stability and efficiency. This research provides a robust framework for understanding complex supply chain dynamics and offers practical solutions to enhance supply chain resilience and flexibility.

In this paper, we investigated a three-dimensional chaotic system that models key aspects of a monetary system, including interest rates, investment demand, and price levels. The proposed system is described by a set of autonomous quadratic ordinary differential equations. We analyze the dynamic behavior of this system through equilibrium points and their stability, Lyapunov exponents (LEs), and bifurcation diagrams. The system demonstrates a variety of behaviors, including chaotic, periodic, and equilibrium states depending on parameter values. Additionally, we explore the multistability of the system and present a radial basis function neural network (RBFNN) controller design to stabilize the chaotic behavior. The effectiveness of the controller is validated through numerical simulations, highlighting its potential applications in economic and financial modeling.

The study revisits the well-known Bouali chaotic financial model, which is characterized by nonlinear dynamics. As a benchmark, the nonlinear feedback control method is implemented and compared with an Adaptive Neuro-Fuzzy Inference System (ANFIS) controller. The ANFIS model is trained using 250 data samples derived from the nonlinear feedback controller and divided into training, validation, and testing subsets. The proposed ANFIS controller demonstrates superior stabilization performance by effectively eliminating chaotic behavior, ensuring stability, and achieving faster convergence than the traditional nonlinear feedback method. Quantitative results confirm this improvement: the ANFIS controller achieved very low Root Mean Square Error (RMSE) values, such as 8.78×10−5 for training and 1.37×10−4 for validation in the profit control input, highlighting its learning accuracy. Additionally, the ANFIS maintained stability even with a reduced number of controllers, demonstrating robustness and adaptability. These findings emphasize the potential of ANFIS controllers to provide efficient and reliable chaos control in complex financial systems.