Complex Dynamics in Non-linear Real Estate Models

Abstract

In the present paper we study the complex dynamics of non-linear cobweb models of real estate markets in discrete time. Our model incorporates two sub-markets, land and housing, interacting with each other. We start by outlining the basic model, which assumes that land prices determine housing supply. This provides the foundations for the development of the more refined and complicated models that follow. These explore the dynamics of the real estate system, when land supply is affected by housing prices. Two forms of this relation are examined: linear and quotient, in order to investigate the dynamics of the system and the qualities and behaviour of the solutions. Stability analysis is obtained in order to investigate the stability properties of the fixed points. Various numerical simulation tools are used in order to study the complex dynamics of the systems. Finally, a global bifurcation occurring in the nonlinear case (quotient) is investigated, which changes the asymptotic behaviour of the system leading from a situation of bistability (cycle of period 2) to chaotic behaviour.