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

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.