Living in a network of scaling cities and finite resources

A modified Lotka-Volterra system in which multiple consumers and resource systems are connected by both consumer-consumer and consumer-resource links. Consumers represent cities, and thus exhibit nonlinear scaling behaviors as population increases w.r.t. harvest rate and harvest conversion efficiency. Populations can also migrate between cities along a welfare-dependent gradient.

Analysis of the model for a simple dyadic network reveals that the basic Lotka-Volterra formulation can lead to stable dynamics, but the inclusion of nonlinear scaling behaviors leads to marked instability. Equilibrium welfare is much more sensitve to scaling of the parameter governing resource use than the parameter for resource harvest intensity. 

Analysis of the model for networks of three or more nodes reveals that connections between cities through resource systems are often more important than direct connections between cities in shaping the dynamics of the system. Local network structures alone are not sufficient for predicting long run dynamics of a particular city, which emphasizes the importance of modeling nested feedbacks between local and global network structures.