Capital Flight and Regional Divergence in a Spatial Model of Financial Contagion

ABSTRACT

This paper investigates a reaction–diffusion–chemotaxis model describing the interaction between financial instability and spatial economic differentiation. The model incorporates a herding mechanism that amplifies speculative behavior and a chemotactic flux representing capital reallocation in response to expected returns net of perceived risk. We first establish the well‐posedness of the system and derive the existence of global classical solutions under suitable conditions. The existence and stability of spatially homogeneous equilibria are then analyzed, and a critical threshold for the chemotactic sensitivity governing the onset of diffusion‐driven instability is obtained. When the net avoidance coefficient exceeds this threshold, the homogeneous coexistence equilibrium is stable; below a positive threshold, it is spatially unstable, and local bifurcation analysis yields non‐constant steady states. The resulting spatial patterns correspond to localized speculative regions and capital‐intensive productive areas. Numerical simulations are provided to corroborate the analytical results and to illustrate the role of endogenous feedback between financial behavior and capital mobility in generating persistent spatial heterogeneity.