A Dynamical Systems Model of Port–Industry–City Co-Evolution Under Data Constraints

This study develops a dynamical systems framework for analyzing the co-evolution of port–industry–city (PIC) systems, with particular attention to the data-limited contexts often encountered in developing coastal regions. The model integrates time-delay differential equations and stochastic disturbances to capture nonlinear behaviors such as investment cycles, policy lags, and external shocks. By introducing dimensionless indicators and dynamic parameter adjustment, the framework reduces dependence on extensive datasets and enhances cross-regional applicability. The Kribi Deep Seaport in Cameroon serves as an illustrative case, demonstrating how the approach can reveal emergent trajectories under alternative development regimes. Simulation results identify three distinct pathways: capital-driven expansion with risks of premature overinvestment, industrial clustering modes requiring coordinated urban services, and policy-led strategies constrained by ecological thresholds and institutional inertia. Compared with conventional static or equilibrium-based models, this approach provides a mathematically rigorous tool for examining delay-driven, nonlinear interactions in complex socio-ecological systems. The framework highlights the value of dynamical systems analysis for scenario exploration, policy design, and sustainable governance in resource-constrained environments.