Nonlinear Dynamics, Innovation and Metropolitan Development

Abstract

This chapter describes the effects of innovation on metropolitan development in terms of the mathematics of nonlinear dynamics. Its main methodological message is that the analysis of these effects can be conducted productively as an unexpected, exogenously induced, perturbation of paths. Such perturbation could lead either to phase transitions and a change of state for the metropolitan area concerned, or to divergencies in dynamic trajectories. Path disturbance, imposed either as an outside shock or as an endogenous event in metropolitan development, could be depicted either by changes in model parameters or the altering of initial conditions. Whereas parameter change may be attributed to basic innovation (which is always exogenous), disturbances of initial conditions can be due at times to endogenous marginal innovation. Both can bring about phase transitions, whereas marginal innovations may be responsible for divergencies. The focus of this chapter is on the marginal type, as they seem to be much more likely to occur than the basic ones, although they have rather confined impacts.