Dynamics and Complexity of Cities

This chapter explains cities as dynamical systems that evolve over time with nonlinear interactions among their constituting components giving rise to complex structures and processes at the macro and micro levels. To make digital twins a facilitator for our understanding of and decision making in cities, dynamics and complexity must be incorporated into digital twins of cities. Our mission is to instil urban theories, particularly those on the dynamic and complex processes, into digital twins of cities. It is of paramount importance to make digital twins urban-theory-based or -informed. With dynamics and complexity in place, we can then capitalize on the power of our information infrastructure to make more appropriate modeling, simulation, monitoring, and management of emergent urban developments in space and time. Since dynamical models are generally complex and high-dimensional, the search for their simplified representations on the low-dimensional manifold is instrumental in the construction of the corresponding digital twins and the mitigation of computational complexity. It is argued that reduced-order model, the low-fidelity model, for high-dimensional construct, the high-fidelity model, plays a crucial role in the efficient and successful simulation of fast and slow urban dynamics, particularly those which are difficult to comprehend and manage, via the digital twins of cities.