Dynamics and Machine Learning Prediction in the Novel Chaotic Financial Firm Model

This paper presents the development and analysis of a Novel Financial Firm Model (NFFM) exhibiting chaotic behavior. Building upon Bouali’s 2002 chaotic financial model, we introduce modifications to the differential equations, resulting in a novel 3-dimensional chaotic system. The dynamics of the proposed model are investigated through various analytical techniques, including dynamical analysis, revealing the system’s capability to display both chaotic and periodic behaviors across different parameter ranges. Furthermore, our study highlights the presence of multistability and coexisting attractors, demonstrating the model’s complex dynamic behavior. This study investigates the 5-step ahead prediction of a newly proposed chaotic model using Support Vector Machine (SVM), k-Nearest Neighbors (KNN), and Long Short-Term Memory (LSTM) models. The prediction performance of the proposed approaches is quantitatively evaluated using the mean squared error (MSE) criterion. The obtained results demonstrate that the KNN model achieves the highest prediction accuracy for the P and F state variables, with MSE values of 8.2495e−7 and 1.1575e−6, respectively, highlighting its effectiveness in capturing the local dynamics of the chaotic system. In contrast, the LSTM model provides superior performance for the R state variable, achieving an MSE of 1.117e−4. This research constructs the NFFM and showcases the effectiveness of machine learning techniques in predicting complex dynamic behaviors, offering valuable insights for both theoretical exploration and practical financial applications.