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.
