The walkway mats usually don't need to be secured in place because they are large and heavy. And truth be told, the stair mats also don't really slide around, but every application is different. So, what if you want to secure the stair mats in place? The best solution would be to use screws that are appropriate for that specific surface (i.e. wood screws, concrete screws, etc.). Only place screws in the grommet holes of the mats. Placing them elsewhere will damage the wiring and void your warranty.
However, some customers are hesitant to make holes in their brand new fancy decks, or their beautiful blue stone steps. And this is understandable. There is another option. We've tested a great outdoor "Rug Gripper Sheet" that can be placed under the stair mats to keep them from sliding. They work great when it's dry and when it's wet on all types of surfaces (wood, composite decking, stone, concrete, etc.) These "Gripper Sheets" leave a little residue at the end of the season, but it washes off easily, and doesn't harm the surfaces they are sticking to.
Below are 2 size options that could work for you. They are also available at other retailers.