  In nonlinear systems analysis, minor fractions of higher-order dynamics are
often neglected for simplicity. Here, we show that machine epsilon levels of
parasitic higher-order dynamics due to computer roundoff alone can cause
divergence of the H\'enon attractor to new attractors or instability. The
divergence develops exponentially regardless of whether the original or new
attractor is chaotic or not. Such singular perturbation by parasitic
higher-order dynamics is a novel property of nonlinear dynamics that is of wide
practical significance in dynamical systems modeling, simulation and control.
