Transient and Asymptotic Dynamics of a Bioeconomic Fishery Model with Market Price Fluctuation and Effort Capacity...

Bioeconomic systems are inherently governed by fast-slow dynamics, arising from the interplay between rapid market adjustments and slower ecological processes. In this paper, we analyze a four-dimensional fishery model that couples predator-prey dynamics with fishing effort subject to capacity constraints and market-clearing prices. Using geometric singular perturbation theory, we show that the separation of timescales leads to a split critical manifold. The system's operational mode is determined by a single dimensionless bioeconomic parameter, which acts as a structural selector between an Internally-Regulated regime and a Capacity-Saturated regime. Beyond equilibrium stability, we focus on transient behaviors by deriving a closed-form approximation for the transient response time to external shocks. This analytical metric explicitly links recovery duration to the effective net growth budget. Our results demonstrate that while the Capacity-Saturated regime may sustain a stable equilibrium, it incurs significantly larger cumulative ecological deficits and slower recovery rates following perturbations. These findings quantify the trade-off between harvest intensity and system responsiveness, offering a dynamical basis for the vulnerability of high-effort fisheries.