Advice on reusing images/illustrations from an AIMS paper I'm working on a chemistry paper about the Belousov-Zhabotinsky-reaction (a chemical oscillator). 

On of my sources is this paper from the AIMS. In the paper the authors have a few figures, especially figure 2 (you can view it on the website). If permitted by the copyright, I would like to include the figure. 

I've no idea how the copyright is regulated with such papers. The AIMS website provides even an option to download the full-size figure. 

What is the copyright for DOI-papers (by the AIMS)? And how can I determine such a thing the next time (if it has an DOI)?

For this specific case, is it allowed to include the figure, on the condition of correct reference?
In general the authors will have assigned all copyright for figures to the journal upon submission/publication. I'm not familiar with the journal in question but it does not look to be any different from any I've ever seen (it has a title, volume, page number etc so is 'normally' citeable). If you wish to reproduce figures from any journal or other source then you need to contact the publisher. This is usually just a formality. 

In this case the contact page for the AIMS (https://www.aimsciences.org/common_news/column/contact) indicates you should get in touch with the Editorial Manager - editorial@aimsciences.org "Regarding the book/journal editorial process, book orders, Printed version claims, copyrights" (emphasis mine)