  We theoretically address minimal search strategies of active, self-propelled
particles towards hidden targets in three-dimensional space. The particles can
sense if a target is close, e.g., by detecting signaling molecules released by
a target, but they cannot deduce any directional cues. We focus on composite
search strategies, where particles switch between extensive outer search and
intensive inner search; inner search is started when the proximity of a target
is detected and ends again when a certain inner search time has elapsed. In the
simplest strategy, active particles move ballistically during outer search, and
transiently reduce their directional persistence during inner search. In a
second, adaptive strategy, particles exploit a dynamic scattering effect by
reducing directional persistence only outside a well-defined target zone. These
two search strategies require only minimal information processing capabilities
and a single binary or tertiary internal state, respectively, yet increases the
rate of target encounter substantially. The optimal inner search time scales as
a power-law with exponent -2/3 with target density, reflecting a trade-off
between exploration and exploitation.
