The current numerical solutions of most engineering problems are obtained on computers based on the classical von Neumann architecture where a set of instructions are executed in a sequential or serial fashion. The utilization of computers to tackle more and more complicated problems requires that there be a continued increase in computational speed. However, the "von Neumann bottleneck", the serial nature of the computer system itself, is the restriction. The present supercomputers with vector processing, special arithmetic/logic units, etc. is one approach. Despite the power and speed of supercomputers, such systems will rely on a basically serial execution of instructions and their capabilities are approaching the physical limitations imposed by the speed of light and quantum mechanical effects. Recent developments in computer science indicates that the parallel processing has the most promising and viable computer architecture for significant improvements in computational performance. Such systems use a large number of processors, each of which is assigned one computational task. Since the processors execute computations simultaneously, the potential computational speed is far than the serial systems. As yet there is very little application software for engineering problems on parallel systems. The goal of this Engineering Initiation project will be to apply parallel computations to nonlinear dynamical system. Efficient parallel processing software will be developed including; cell mapping techniques for analysis and synthesis of optimal control, bifurcation curves for two and three degrees of freedom systems, and implement and test the algorithms on FLEX/32 Parallel computer at the University of Southern California.