Stochastic bifurcation in economic growth model driven by L\'evy noise

Abstract

This paper enhances the classical Solow model of economic growth by integrating L\'evy noise, a type of non-Gaussian stochastic perturbation, to capture the inherent uncertainties in economic systems. The extended model examines the impact of these random fluctuations on capital stock and output, revealing the role of jump-diffusion processes in long-term GDP fluctuations. Both continuous and discrete-time frameworks are analyzed to assess the implications for forecasting economic growth and understanding business cycles. The study compares deterministic and stochastic scenarios, providing insight into the stability of equilibrium points and the dynamics of economies subjected to random disturbances. Numerical simulations demonstrate how stochastic noise contributes to economic volatility, leading to abrupt shifts and bifurcations in growth trajectories. This research offers a comprehensive perspective on the influence of external shocks, presenting a more realistic depiction of economic development in uncertain environments.