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<p>Bioeconomic systems are inherently governed by <b>fast–slow dynamics</b>, 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 <b>capacity constraints</b> and market-clearing prices. Using <b>geometric singular perturbation theory</b>, we show that the separation of timescales leads to a <b>split critical manifold</b>. 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 <b>transient response time</b> 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Zhehao Liu,
  • Wenjun Liu,
  • Xuebing Zhang,
  • Ali Moussaoui,
  • Pierre Auger

摘要

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.