A chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same reaction. Many forms of autocatalysis are recognized. A set of chemical reactions can be said to be "collectively autocatalytic" if a number of those reactions produce, as reaction products, catalysts for enough of the other reactions that the entire set of chemical reactions is self-sustaining given an input of energy and food molecules (see autocatalytic set). Acid-catalyzed hydrolysis of esters produces carboxylic acids that also catalyze the same reaction. Indeed, the observation of an accelerating hydrolysis of gamma valerolactone to gamma-hydroxyvaleric acid led to the introduction of the concept of autocatalysis in 1890. The oxidation of hydrocarbons by air or oxygen is the basis of autoxidation. Like many radical reactions, the rate vs time plot shows a sigmoidal behavior, characteristic of autocatalysis. Many reactions of organic compounds with halogen involve autocatalytic radical mechanisms. For example the reaction of acetophenone with bromine to give phenacyl bromide. Oscillating reactions such as the Belousov-Zhabotinsky reaction are more complicated examples that involve autocatalysis. In such reactions the concentrations of some intermediates oscillate, as does the rate of formation of products. Other notable examples are the Lotka–Volterra equations for the predator-prey model, and the Brusselator model. Autocatalysis applies also to reactions involving solids. Crystal growth provide dramatic examples of autocatalysis: the growth rate depends on the surface area of the growing crystal. The growth of metal films from solution using the technique of electroless plating is autocatalytic. The rate of plating accelerates after some deposition has occurred, i.e., nucleation. Autocatalytic reactions are those in which at least one of the products is also a reactant. A simple autocatalytic reaction can be written with the rate equations (for an elementary reaction) This reaction is one in which a molecule of species A interacts with a molecule of species B.