Hi,
Table RSLOGSYSMAP is used during transport (more precisely after-import) of a source system dependent object. E.g. a DataSource. The table must be maintained in the BW system. In your case the APO BI system.
Table RSLOGSYSMAP must contain all conversion rules (using logical system names (e.g. BWDCLNT400) for the respective environment. I.e. source system Development (e.g. ECC Development) to source system Quality (e.g. ECC Quality) and BW Development to BW Quality.
Please also refer to SAP Help.
Best regards,
Sander