The butterfly effect in economics: Exploring chaos with a simple financial model

Authors

Sandy HS Herho, University of California, RiversideFollow

Publication Date

2-13-2026

Keywords

Chaotic dynamics, Financial system, Lyapunov exponent, Sensitivity analysis, Python

Disciplines

Mathematics | Non-linear Dynamics | Numerical Analysis and Computation | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

Wild swings in financial markets need not result from external shocks like earthquakes or wars—they can emerge from deterministic chaos. This article introduces kalimusada, an open-source Python library that lets students and instructors explore this phenomenon through a simple three- equation model of financial dynamics. The model couples interest rates, investment, and prices through nonlinear feedback, generating bounded but unpredictable oscillations characteristic of chaos. Tiny differences in starting conditions—smaller than any measurement could detect—grow exponentially until two initially identical economies follow completely different paths. The library provides ready-to-use tools for visualizing this “butterfly effect” in economics, computing divergence metrics, and estimating Lyapunov exponents. Available via PyPI with source code on GitHub, kalimusada serves as a pedagogical gateway to chaos theory through an economically motivated example accessible to anyone familiar with ordinary differential equations.

Recommended Citation

Herho, Sandy HS (2026) "The butterfly effect in economics: Exploring chaos with a simple financial model," CODEE Journal: Vol. 20: Iss. 1, Article 1.
Available at: https://scholarship.claremont.edu/codee/vol20/iss1/1

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.