<p>Nonlinear financial mathematical systems frequently exhibit strong feedback mechanisms, sensitivity to initial conditions, and chaotic regimes, which complicate their numerical approximation using conventional (analytical and numerical) solvers. This study introduces a Morlet Wavelet Neural Network (MWNN) trained through a hybrid heuristic procedure that integrates Particle Swarm Optimization with the Neural Network Algorithm. The intelligent method is employed to approximate the trajectories of an established integer-order chaotic model based on financial describing the coupled evolution of short-term interest rates, investment demand, and price indices. The using MWNN structure suited to capturing oscillatory and rapidly varying behavior, while the hybrid optimization approach strengthens global search capacity and promotes stable convergence. Three representative dynamical scenarios are investigated, and the MWNN approximations are assessed against high-accuracy with reference solutions. A statistical evaluation based on multiple independent runs using absolute errors, standard deviation, mean squared error and Theil’s inequality coefficient, these shows that the proposed framework yields accurate and consistently reliable results across all cases. These findings underscore the effectiveness of MWNN architectures combined with heuristic optimization for modeling nonlinear financial dynamics and provide a basis for future extensions to more complex systems, including those with memory effects or higher dimensionality.</p>