Within the framework of the assembly-type catastrophe model, a nonlinear dynamic equation (DE) homogeneous in the parameter η {t} with an aftereffect is constructed, in which η {t} characterizes the deviation of the reduced density of a thin surface layer on the liquid-vapor interface from the mean density of the vapor-liquid system. This equation is used to treat a second-order nonlinear DE with a variable damping coefficient for a vapor-liquid system excited by periodic "impacts" (acts of evaporation and condensation of molecules). This DE is integrated over a finite time interval to find a two-dimensional mapping whose numerical solution describes the chaotic dynamics of the density in time, including "homophase" and "heterophase" fluctuations. For this system, the bifurcation diagrams are constructed and the Lyapunov exponents are found.