Approach-avoidance conflicts were one of the earliest applications of catastrophe theory. Empirical studies evaluating the cusp catastrophe model for approach-avoidance dynamics have only started to appear recently, however. The present study reviews the extant research and expands the concept to approach and avoidance coping styles. Research participants were 333 adults from the general population recruited through Amazon Mechanical Turk. They completed measures of psychological symptoms, quality of life (QOL), approach and avoidance coping styles, and COVID-related stress. Cusp models for symptoms (R2 = .84) and QOL (R2 = .89) illustrated approach and avoidance functioning as bifurcation gradients for both psychological symptoms and QOL. Both models provided more accurate representations of the data than the linear alternatives (R2 = .54 and .24 respectively), thus providing further support for the cusp dynamics. The cusp catastrophe model has extensive applicability to approach-avoidance behaviors. There was greater variability (hysteresis) in outcomes for people who used fewer coping strategies of either the approach or avoidance types.