Here is an Internet resource I came across recently:

Barkley Rosser's Home Page

Barkey Rosser, Jr. is an professor of economics at James Madison University. The home page lists a number of writings on non-linear dynamics, complex systems and economics.

The paper that initially drew my attention: "Aspects of Dialectics and Nonlinear Dynamics". "Among the deepest problems in political economy is that of the qualitative transformation of economic systems from one mode to another... this paper will argue that nonlinear dynamics offers a way in which a mathematical analogue to certain aspects of the dialectical approach can be modelled, in particular, that of the difficult problem of qualitative transformation..."

"In most linear models, continuous changes in inputs do not lead to discontinuous changes in outputs, which will be our mathematical interpretation of the famous 'quantitative change leading to qualitative change' formulation."

The paper reviews basic dialectical concepts; discusses how catastrophe theory can imply dialectical results; considers chaos theory from a dialectical perspective; and examines some emergent complexity concepts along similar lines, "culminating in a broader synthesis."