The seminar will be focused on the nonlinear nuances present in the equations governing the evolution of particle size during activation and deactivation of cloud condensation nuclei (CCN). A fixed-point analysis of the nonlinear dynamical system embodied in the drop growth laws reveals that the system undergoes the so-called saddle-node bifurcation and a cusp catastrophe. The control parameters chosen for the analysis are the relative humidity and the particle concentration. Leveraging results from bifurcation theory and conceptualising CCN activation as coalescence (sic!) of the fixed points in the dynamical system, an analytical estimate of the activation timescale is derived through 
estimation of the time spent in the so-called saddle-node bifurcation bottleneck. Numerical integration of the system coupled with a simple air-parcel cloud model portrays two types of activation/deactivation hystereses: one associated with the kinetic limitations on droplet growth when the system is far from equilibrium, and one occurring close to equilibrium and associated with the cusp catastrophe. Aerosol concentration threshold for hysteretic behaviour stemming from the cusp catastrophe is confirmed with the parcel model simulations. Relevance of the presented analyses in the context of the development of particle-based models of aerosol–cloud interactions will be highlighted. Work based on Arabas & Shima 2017 (Nonlin. Processes Geophys., 24, doi:10.5194/npg-24-535-2017).