Our research is on nonlinear and chaotic dynamical systems which are unpredictable even without random perturbations that are inherent in nature. We employ multiple-scale asymptotics and numerical bifurcation analysis to investigate nonlinear interactions in continuum mechanical systems and employ chaos theory to determine the nature of instabilities governed by sensitivity-to-initial-conditions. Applications include nano-resonator arrays and fluid-structure-interaction systems where complex spatio-temporal dynamics and self-excited dynamics are governed by global bifurcations.