Catastrophe theory

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...

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...

Imperfection-sensitivity and Catastrophe Theory

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...

Examining the theory of error catastrophe.

This discussion attempts to present a simple explanation of the current theory of error catastrophe and why it does not herald a paradigm shift in antiviral strategy. In the main text of the paper, the workings of a simple model of error catastrophe are examined to demonstrate what actually causes error catastrophe. The Appendix contains a more detailed discussion of the original error threshol...