In this paper, we proposed and analyzed a novel chaotic monetary model by extending Lazureanu's three-dimensional economic system through the introduction of a fourth state variable, the Expectation Index (E_i), which captures psychological and behavioral dynamics in financial decision-making. The modified system exhibits rich dynamical features such as chaos, multistability, coexisting attractors, and complex bifurcation behavior. Key parameters influencing chaotic regimes were investigated through bifurcation diagrams and Lyapunov exponent spectra. Furthermore, the model's behavior was controlled using amplitude scaling and DC offset boosting techniques without altering its chaotic structure. To suppress chaos and achieve stabilization, a Supervised Radial Basis Function Neural Network (SRBFNN) controller was designed. The SRBFNN was trained using system error signals, achieving extremely low mean squared error (MSE) values: 1.14543×10⁻²¹, 1.7698×10⁻²¹, 2.38218×10⁻¹⁹, and 6.16987×10⁻²⁰ across the four networks. Simulation results demonstrated that the SRBFNN effectively eliminates chaotic behavior and drives the system toward desired equilibrium states with high accuracy and stability.