Catastrophe Theory and Caustics

Catastrophe Theory and Urban Processes

Phenomena exhibiting discontinuous change, divergent processes, and hysteresis can be modelled w i t h catastrophe theory, a recent development in differential topology. Exposition of t h e theory is illustrated by qualitative interpretations of the appearance of functions i n central place systems, and of price cycles for urban housing. Catastrophe Theory and Urban Processes John Casti and Har...

Imperfection-sensitivity and Catastrophe Theory

Transformation invariant stochastic catastrophe theory

Catastrophe theory is a mathematical formalism for modeling nonlinear systems whose discontinuous behavior is determined by smooth changes in a small number of driving parameters. Fitting a catastrophe model to noisy data constitutes a serious challenge, however, because catastrophe theory was formulated specifically for deterministic systems. Loren Cobb addressed this challenge by developing a...

Catastrophe theory in Dulac unfoldings

In this paper we study analytic properties of compensator and Dulac expansions in a single variable. A Dulac expansion is formed by monomial terms that may contain a specific logarithmic factor. In compensator expansions this logarithmic factor is deformed. We first consider Dulac expansions when the power of the logarithm is either 0 or 1. Here we construct an explicit exponential scaling in t...

Catastrophe Theory and the Business Cycle

In this paper we examine a variation on Kaldor’s (1940) model of the business cycle using some of the methods of catastrophe theory. (Thom (1975), Zeeman (1977)). The development proceeds in several stages. Section I provides a brief outline of catastrophe theory, while Section II applies some of these techniques to a simple macroeconomic model. This model yields, as a special case, Kaldor’s bu...