What is autocatalyst? Give examples.

Hint: As known that the catalyst is a substance which reacts with the reactants followed by an intermediate form which facilitates the product formation. If the product formed itself acts as a catalyst and alters the rate involving self-catalysis.

Complete step by step solution:
A catalytic reaction in which no specific external catalyst is added, so during the initial stage, the reaction is slow forming the product whose existence then increases the reaction rate. Thus, the reaction product acts as the catalyst itself in the reaction. This self-catalysis process is called autocatalysis.
A reaction showing autocatalysis is as follows:
-In the reaction of ethanedioic acid or oxalic acid with acidified (that is, with dilute sulphuric acid in) potassium permanganate. The oxidation reaction of the oxalic acid occurs by the potassium permanganate having $M{{n}^{7+}}$ oxidation state which is reduced to $M{{n}^{2+}}$ state acting as a catalyst.
The overall reaction occurring is: $5{{H}_{2}}{{C}_{2}}{{O}_{4}}+2KMn{{O}_{4}}+{{H}_{2}}S{{O}_{4}}\to 2MnS{{O}_{4}}+{{K}_{2}}S{{O}_{4}}+10C{{O}_{2}}+8{{H}_{2}}O$
- In the initial stage of the reaction, due to the repulsion between the two negative ions $MnO_{4}^{-}\text{ and }{{C}_{2}}O_{4}^{2-}$, leading to the higher activation energy. The rate of reaction is slow and the decolourisation of the purple colour of $KMn{{O}_{4}}$ occurs after a time lag.
-But, in this step the $M{{n}^{2+}}$formed acting as the catalyst is oxidised to $M{{n}^{3+}}$and this $M{{n}^{3+}}$supplements the $Mn{{O}_{4}}^{-}$ in the oxidation of oxalic acid.
The reaction pathway through the $M{{n}^{3+}}$ intermediate is as follow:
\[4M{{n}^{2+}}+MnO_{4}^{-}+8{{H}^{+}}\to 5M{{n}^{3+}}+4{{H}_{2}}O\]
\[2M{{n}^{3+}}+{{C}_{2}}O_{4}^{2-}\to 2C{{O}_{2}}+2M{{n}^{2+}}\]
This intermediate reaction thus, lowers the activation energy. Hence, the decolourisation now becomes instantaneous with addition of more potassium permanganate as the rate of reaction increases.

Note: In this catalytic process, involving alteration of the rate of reaction and is regenerated back at the end. The autocatalyst also eases the process and makes it efficient.