This paper describes the implementation of a dynamical systems approach to aeroelastic analysis using the Connection Machine model 2 (CM‐2). Through numerical simulation, the regions of harmonic and chaotic behavior in the δ,R_x (velocity, in‐plane load) plane have been examined in detail. These regions are of interest in evaluation of the fatigue life of fluttering plates. The CM‐2 computer architecture allows the removal of many of the previous simplifying and limiting assumptions regarding the prediction of the stability regions maps. Owing to its high‐speed prediction capability, the CM‐2, with framebuffer, offers 'real‐time' display of the solution as it evolves during the prediction process. This feature gives insight into the fundamental way in which the solution evolves. This is essential in defining the scenarios describing roads to chaotic behavior of the dissipative dynamical systems.