Date of Award

2025

First Advisor

Dr. Daniel Neilson

Second Advisor

Dr. Amanda Landi

Abstract

This thesis develops a discrete-time dynamical systems framework for analyzing cargo f low in port networks under two ship routing paradigms. The two models are; 1) a rotational routing scheme, in which ships follow a fixed loop through a sequence of ports, and 2) a hub-and-spoke model, in which a central hub coordinates distribution to peripheral ports. Each port maintains a warehouse with fixed maximum capacity, external inflow, and scheduled outflow. Ships transfer cargo between ports under constraints on capacity, transfer rate, and travel time. Through simulation and mathematical analysis, the nonlinearity of the systems is dissected using tools from dynamical systems analysis. Fixed point behavior is characterized under both routing regimes, and local stability is examined via lin earization techniques. The rotational model is shown to require a global flow balance for equilibrium, rendering it fragile to perturbations. In contrast, the hub-and-spoke model exhibits decentralized stability, with each port stabilizing independently given sufficient ship service

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