Final answer:
The polygynous mating system is where one male mates with many females, with the female primarily responsible for offspring care, as seen in species like the yellow-rumped honeyguide and sage grouse.
Step-by-step explanation:
The mating system described where one male bonds with many females but only at one time is known as the polygynous mating system. In polygyny, one male mates with multiple females, and the female is primarily responsible for parental care due to the male's inability to provide care for many offspring. The polygynous system takes different forms, such as resource-based polygyny, where males compete for territories to attract females, harem mating structures as seen in elephant seals, and lek systems where males display to females in a communal area. Examples in nature include the yellow-rumped honeyguide and the sage grouse.