The Predator-Prey Model of Tax Evasion: Foundations of a Dynamic Fiscal Ecology

Tax evasion is a dynamic process reflecting continuous interaction between taxpayers and regulatory institutions rather than a static deviation from fiscal equilibrium. This study introduces a predator-prey model of tax evasion that translates the Lotka-Volterra framework from biology into budgetary dynamics. The model captures the feedback between the volume of tax evasion and the intensity of regulation, incorporating nonlinearity, implicit reactive lag, and adaptive response. Theoretical derivation and numerical simulation identify three dynamic regimes—stable equilibrium, limit-cycle oscillation, and instability—that arise through a Hopf bifurcation. Bifurcation maps in the (r, a), (r, b), and (r, c) parameter spaces reveal how control efficiency, institutional inertia, and behavioral feedback jointly determine fiscal stability. Results show that excessive enforcement may destabilize the system by inducing regulatory fatigue, while weak control enables exponential growth in evasion. The model provides a dynamic analytical tool for evaluating fiscal policy efficiency and identifying stability thresholds. Its findings suggest that adaptive, feedback-based regulation is essential for maintaining long-term tax discipline. The study contributes to closing the research gap by providing a unified dynamic framework linking micro-behavioral decision-making with macro-fiscal stability, offering a foundation for future empirical calibration and behavioral extensions of fiscal systems.