A robust spectral integral method for solving chaotic finance systems

Abstract

Nonlinear chaotic finance systems are represented by nonlinear ordinary differential equations and play a significant role in micro-and macroeconomics. In general, these systems do not have exact solutions. As a result, one has to resort to numerical solutions to study their dynamics. However, numerical solutions to these problems are sensitive to initial conditions, and a careful choice of the suitable parameters and numerical method is required. In this paper, we propose a robust spectral method to numerically solve nonlinear chaotic financial systems. The method relies on spectral integration diagonal matrices coupled with a domain decomposition method to preserve the high accuracy of our methodology on a long time period. In addition, we investigate stability of chaotic finance systems using the Lyapunov theory, and a two sliding controller mode synchronisation to regulate the synchronisation of these systems. Numerical experiments reveal the high accuracy and the robustness of our method and validate the synchronisation of chaotic finance systems.