In the foreground of the picture, you can see a brown region.  This is a different type of grass than the buffalo that makes up the remainder of the lawn.

[![lawn][1]][1]

I would like the whole lawn to be buffalo for a consistent look.  How can I achieve this? 

This small area of different grass has persisted for a number of years.  It looks brown now as there has not been any rain for about 10 days.  When it rains, it will come back green again.

The buffalo seems to grow better in summer, while the other grass grows better when it is colder.  It's spring here now so I thought it might be a good time to address this.

Can I spray this with round-up, and allow the buffalo to grow in from the edges.  Do I need to physically dig it up?

  [1]: https://i.sstatic.net/EiJyi.jpg