Table of Contents
Journal of Artificial Evolution and Applications
Volume 2008, Article ID 745694, 8 pages
Research Article

Generating Complete Bifurcation Diagrams Using a Dynamic Environment Particle Swarm Optimization Algorithm

Programa de Graduados e Investigación en Ingeniería Eléctrica, Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria, Morelia Michoacan 58030, Mexico

Received 20 July 2007; Accepted 28 November 2007

Academic Editor: Jim Kennedy

Copyright © 2008 Julio Barrera et al. 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.


A dynamic system is represented as a set of equations that specify how variables change over time. The equations in the system specify how to compute the new values of the state variables as a function of their current values and the values of the control parameters. If those parameters change beyond certain values, the system exhibits qualitative changes in its behavior. Those qualitative changes are called bifurcations, and the values for the parameters where those changes occur are called bifurcation points. In this contribution, we present an application of particle swarm optimization methods for dynamic environments for plotting bifurcation diagrams used in the analysis of dynamical systems. The use of particle swarm optimization methods presents various advantages over traditional methods.