Several stays: many-to-many relationship
Based on your diagram above what you have is a one to many, not a many to many relationship.  You have your Researcher table and your Stay table.  If you add the researcher id in the stay table to the primary key you have a relationship of:

Researcher.ResearcherId -> Stay.ResearcherId 

Where a given researcher can have multiple stays.  For example

Researcher John Smith has an Id of 2.

In the stay table you would have

From       Till       ResearcherId
1/1/2013   1/5/2013   2
2/6/2013   3/1/2013   2


etc