A Bifurcation Diagram Tool based on NichePSO

A software tool for bifurcation diagram plotting called BDT (Bifurcation Diagram Tool) is presented. CDT is based on NichePSO, a meta-heuristic capable of optimizing functions. The problem of determining a fixed point is reformulated as one of finding the minimum of another function. Niches are used to determine all fixed points of the function. The stability of the fixed points found by PSO is determined use linearization (when it is feasible). BDT offers the following advantages over existing software: portability - developed in Java and Scala, installation and deployment is straightforward; usability - the system is user-friendly, the PSO parameters have been tuned to work with most systems, and no initial conditions are needed to produce BDs; completeness - by using PSO with niches, CDT finds all fixed points of the system most of the time (Auto, requires initial conditions and follows a line of the BD, thus producing a subset of the BD of any Dynamical System).