Many urban phenomena exhibit remarkable regularity in the form of nonlinear scaling behaviors, but their implications on a system of networked cities has never been investigated. Such knowledge is crucial for our ability to harness the complexity of urban processes to further sustainability science. In this paper, we develop a dynamical modeling framework that embeds population-resource dynamics-a generalized Lotka-Volterra system with modifications to incorporate the urban scaling behaviors-in complex networks in which cities may be linked to the resources of other cities and people may migrate in pursuit of higher welfare. We find that isolated cities (i.e., no migration) are susceptible to collapse if they do not have access to adequate resources. Links to other cities may help cities that would otherwise collapse due to insufficient resources. The effects of inter-city links, however, can vary due to the interplay between the nonlinear scaling behaviors and network structure. The long-term population level of a city is, in many settings, largely a function of the city's access to resources over which the city has little or no competition. Nonetheless, careful investigation of dynamics is required to gain mechanistic understanding of a particular city-resource network because cities and resources may collapse and the scaling behaviors may influence the effects of inter-city links, thereby distorting what topological metrics really measure.