Discrete Dynamics in Nature and Society
Volume 1 (1997), Issue 2, Pages 135-146

Ergodic cobweb chaos

Akio Matsumoto

Department of Economics, Niigata University, 8050 2-No-Cho Ikarashi, Niigata 950-21, Japan

Received 9 October 1996

Copyright © 1997 Akio Matsumoto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study augments the traditional linear cobweb model with lower and upper bounds for variations of output. Its purpose is to detect the relationship between the output constraints and the dynamics of the modified model. Due to the upper and lower bounds, a transitional function takes on a tilted z-profile having three piecewise segments with two turning points. It prevents the price (or quantity) dynamics from explosive oscillations. This study demonstrates, by presenting numerical examples, that the modified cobweb model can generate various dynamics ranging from stable periodic cycles to ergodic chaos if a product of the marginal propensity to consume and the marginal product is greater than unity.