Complex and Chaotic Dynamics in Economics

Abstract

Like a limit cycle, a chaotic attractor is a locally unstable but globally stable form of dynamic behavior. Examples of chaotic attractors including the Lorenz attractor, the Rössler attractor, and the logistic system are studied. The deterministic unpredictability of chaotic systems is contrasted with their statistical predictability. Chaotic systems are a tempting model for economics, particularly financial economics.

Complex systems include the cell, the brain and nervous system, the capitalist social division of labor, and the universe. Complex systems theory attempts to understand the general properties of such systems. Systems with stable point attractors or limit cycles cannot sustain long-term evolving structures, which collapse into their limits; chaotic systems also cannot sustain evolving structures because they are dispersed in the divergence of nearby points on chaotic attractors. Type I and II cellular automata provide examples of stable dynamics, and Type III of chaotic dynamics. Type IV cellular automata, which lie on the boundary of stability, exhibit long-term evolving and interacting structures and serve as a paradigm of complex systems. Topology and global interaction have special roles in agent-based models of complex economic interactions. Simulation of agent-based models constitutes a research frontier that can complement and supplement analytical approaches to understanding economic interactions.

Programs implementing a model of spatially decentralized exchange are presented as an example and basis for exercises exploring the issues involved in agent-based models of economic interaction.