page_title: Autocatalysis
section_title: Idealized example: Lotka–Volterra equation
hierarchical_section_title: Autocatalysis / Creation of order / Temporal order / Idealized example: Lotka–Volterra equation
caption_attribution_description: English: A solution to the cheetah/baboon dynamics problem. The solutions correspond to various iterative methods. Note how the solution oscillates near the point (60,25), corresponding to a population of 60 baboons and 25 cheetahs.
context_page_description: A single chemical reaction is said to be autocatalytic if one of the reaction products is also a catalyst for the same or a coupled reaction. Such a reaction is called an autocatalytic reaction.
  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.
context_section_description: Consider a coupled set of two autocatalytic reactions in which the concentration of one of the reactants A is much larger than its equilibrium value. In this case, the forward reaction rate is so much larger than the reverse rates that we can neglect the reverse rates.
  with the rate equations
  .
  Here, we have neglected the depletion of the reactant A, since its concentration is so large. The rate constants for the three reactions are , , and , respectively.
  This system of rate equations is known as the Lotka–Volterra equation and is most closely associated with population dynamics in predator–prey relationships. This system of equations can yield oscillating concentrations of the reaction intermediates X and Y. The amplitude of the oscillations depends on the concentration of A (which decreases without oscillation). Such oscillations are a form of emergent temporal order that is not present in equilibrium.
caption: The Lotka–Volterra equation is isomorphic with the predator–prey model and the two-reaction autocatalytic model. In this example baboons and cheetahs are equivalent to two different chemical species X and Y in autocatalytic reactions.
exif: {}