In this paper, navigation algorithms for a fleet of multiple nonholonomic UAVs capable of evading a chasing predator and also pursuing a desired target are proposed. The proposed biologically-inspired navigation algorithms are used to define path planning trajectories which are tracked by a designed backstepping tracking controller. We implement the group of nonholonomic UAVs in an adaptive network, specifically inspired by the relationship between a school of fish and a predator. This approach approximately simulates an air combat field. To put this in context, the aim is to use a biologically inspired algorithm along with a designed controller to achieve both target pursuance and effective evasion from a predator. This is equivalent to having multiple UAVs on the same mission of attacking a target, while also aware of a predator on pursuit. The UAVs aim to maneuver and evade the predator while also coordinating their movement and behaviors in a cooperative and coherent manner.