Urban Structure Model with Endogenous Flows of Firms and Population

This paper widens the economic context within the framework of urban morphology through the introduction of entrepreneurial activities. Unlike plenty of papers, this one utilizes the standard reaction-convection-diffusion structure for the most part, rather than any kind of Continuous Lattice Models (CLM) or Cellular Automation (CA). Kinetics of the system is the modification of competitive Lotka-Volterra equations, for two homogeneous species: firms and population. Spatial movements are somewhat similar to ones in the Keller-Segel chemotaxis model, meaning that they consist both of diffusion and convection terms. Using linear stability analysis, I get the conditions for pattern generation. Also, the Forward-Time Central-Space discretization scheme is described and used to simulate the model numerically using, the Python programming language. Through simulations, notable symmetry characteristics of patterns were observed and discussed intuitively.