Oscillating vs Autocatalytic reactions

Are all oscillating reactions autocatalytic? Or are all autocatalytic reactions oscillating? What's the relation between them? Am I just mixing up different things or are they basically the same?
For instance, the Belusov-Zhabotinskii is a nice example of an autocatalytic reaction, but it has an oscillating character.




Non-oscillating autocatalytic reactions
---------------------------------------



> 
> [OP] are all autocatalytic reactions oscillating?
> 
> 
> 


No, there are many examples of autocatalytic reactions that don't oscillate. On is given in the comments:



> 
> [Poutnik] Oscillators generally need some positive loopback which destabilizes them. Oscillatory reactions are not exception. E.g. Oxidation of oxalic acid by permanganate is autocatalyzed by manganese(II) ions, but is not oscillatory as there is no such a loopback.
> 
> 
> 


An example that is not strictly chemistry is crystallization. Making sugar candy from a supersaturation sugar solution is faster if you add a stick with a tiny amount of solid sugar on it (a crystallization nucleus). A [similar physical effect](https://www.youtube.com/watch?v=_9N-Y2CyYhM) is agitating a bottle of super-cooled liquid water.


The Wikipedia article on autocatalysis lists chemical reaction examples at the [end of the page](https://en.wikipedia.org/wiki/Autocatalysis#Examples_of_autocatalytic_reactions). One spectacular example is the transformation of metallic tin to the non-metallic gray tin, a process called tin pest. Two examples from biochemistry are the PCR test for SARS-2 viral RNA, and the radical polymerization of acrylamide to form polyacrylamide (the product is used in gel electrophoresis of proteins).


Non-autocatalytic oscillating reactions?
----------------------------------------



> 
> Are all oscillating reactions autocatalytic?
> 
> 
> 


There is an theoretical model discussed in this post, [What's a minimal yet chemically-meaningful kinetic system for an oscillating reaction?](https://chemistry.stackexchange.com/q/267/72973). In its simplest form, it is unrealistic because there is no source of Gibbs energy to continuously drive it (i.e. to make at least one of the reactions virtually unidirectional).


I am not aware of a experimental system that oscillates yet does not contain autocatalytic elements. It is possible that there is one somewhere, but it is not among the two or three systems typically discussed as example for oscillatory reactions.


 5