BIGIP2000s (LTM) firmware upgrade.

You can read 13.1.1 release Notes:

Upgrading from earlier versions

Upgrading from version 11.x or later

When you upgrade from version 11.x or later, you use the Software Management screens in the Configuration utility to complete these steps. To open the Software Management screens, in the navigation pane of the Configuration utility, expand System, and click Software Management. For information about using the Software Management screens, see the online help.

Upgrading from versions earlier than 11.x

You cannot roll forward a configuration directly to this version from BIG-IP version 10.x or earlier. You must be running version 11.x (or later) software. For details about upgrading from earlier versions, see the release notes for the associated release.

Upgrading to 4th element versions from versions earlier than 11.5.0

You cannot directly update from pre-11.5.0 versions (e.g., v11.4.x, v11.2.x, etc.) to any 4th element version (e.g., v12.1.3.1, v13.1.0.1, etc.). Direct upgrade to 4th element versions is supported only from v11.5.0 and later. For pre-11.5.0 versions, you must first upgrade to v11.5.0 or later. The recommended upgrade path is from v11.4.1 to v12.1.3, and then to v12.1.3.1.