BIFURCATIONS AND STABILITY PROPERTIES OF NONLINEAR-SYSTEMS WITH SYMBOLIC SOFTWARE

A sequence of symbolic algebra and algorithms, together with the corre sponding software package, for the nonlinear analysis of vibrations, b ifurcations and stability properties of autonomous and nonautonomous s ystems have been developed. The package has been designed, in particul ar, to handle complex phenomena in the vicinity of compound critical p oints. It also has the capacity to deal with multifrequency excitation s in the framework of nonautonomous systems. The approach is based on a systematic perturbation technique, and it provides a convenient and advantageous tool for the nonlinear analysis of complex phenomena (e.g ., high-dimensional tori). The algebra is presented in two distinct ca tegories, depending on the properties of the Jacobian, characterizing the compound critical point of interest. Thus, the case in which all e igenvalues of the Jacobian are pure imaginary pairs has been treated s eparately from the case involving a combination of imaginary pairs and zero eigenvalues. Specifically, two examples have been analyzed-a for ced system with two pairs of pure imaginary eigenvalues and a system w ith one pair and one zero eigenvalues under combined forcing and param etric excitation.