What factor make a device Active and another Standby, and when Active become standby does it become Active again once a network is stable (or anything that make it standby earlier)
This very much depends on your configuration. According to KB:
The BIG-IP system initiates failover according to any of several events that you define. These events fall into these categories:
System fail-safe
Withsystem fail-safe, the BIG-IP system monitors various hardware components, as well as the heartbeat of various system services. You can configure the system to initiate failover whenever it detects a heartbeat failure.
Gateway fail-safe
Withgateway fail-safe, the BIG-IP system monitors traffic between an active BIG-IP system in a device group and a pool containing a gateway router. You can configure the system to initiate failover whenever some number of gateway routers in a pool of routers becomes unreachable.
VLAN fail-safe
WithVLAN fail-safe, the BIG-IP system monitors network traffic going through a specified VLAN. You can configure the system to initiate failover whenever the system detects a loss of traffic on the VLAN and the fail-safe timeout period has elapsed.
HA groups
With anHA group, the BIG-IP system monitors trunk, pool, or cluster health to create an HA health score for a device. You can configure the system to initiate failover whenever the health score falls below configurable levels.
Auto-failback
When you enableauto-failback, a traffic group that has failed over to another device fails back to a preferred device when that device is available. If you do not enable auto-failback for a traffic group, and the traffic group fails over to another device, the traffic group remains active on that device until that device becomes unavailable.
