Ponente
Descripción
Open-access bioeconomic models have long been used as examples to study the interaction between population dynamics and human exploitation. In their classical formulation, these models assume a constant market price for the harvested resource, leading to autonomous dynamical systems whose long-term behavior is governed by a stationary bioeconomic equilibrium. While analytically convenient, this assumption neglects the fact that real-world resource prices are often subject to external temporal fluctuations driven by seasonal demand, macroeconomic conditions, or institutional factors, which may significantly alter exploitation patterns.
In this work, we investigate the dynamical consequences of introducing exogenous, time-dependent price fluctuations into a classical open-access fishery model of Smith type. From a mathematical biology perspective, the resulting framework can be interpreted as a population system subject to external non-autonomous forcing, where economic variability acts as an environmental driver that modulates the intensity of harvesting pressure.
We show that when price fluctuations are bounded and damped in time, the system is asymptotically autonomous and inherits both local and global stability properties of the bioeconomic equilibrium of the associated autonomous model. This result provides a rigorous justification for the robustness of equilibrium exploitation regimes under transient external perturbations.
In contrast, when price oscillations persist, the system no longer converges to a stationary state. Instead, we prove the existence of stable periodic solutions induced by the external forcing, and, under multi-frequency incommensurate oscillations, the emergence of quasiperiodic dynamics supported on normally hyperbolic invariant tori.
Furthermore, we show that the mean price level acts as a bifurcation parameter, organizing qualitative transitions between null effort, stationary exploitation, and oscillatory regimes. Our results highlight that complex population dynamics, often attributed to intrinsic biological mechanisms, may arise solely from external economic forcing, with important implications for the interpretation of observed cycles in exploited biological populations.