Collective chemotactic search

We investigate collective search by self-propelled agents that are repelled by their own chemically produced trails, a minimal mechanism that simultaneously generates indirect interactions and memory. Using lattice and off-lattice models, we show that this mechanism enhances search efficiency through two distinct regimes. In a weak-memory regime, chemical cues are short-lived and interactions primarily promote spatial separation between agents. This reduces redundant exploration while preserving mobility, leading to an optimal trade-off between spatial order and persistence. In a strong-memory regime, long-lived chemical trails induce effective self-avoidance, strongly suppressing revisits and long search times. Here, optimal search occurs at finite memory strength: Permanently persistent trails lead to self-caging, while moderate memory enables efficient exploration. At higher densities, overlapping chemical trails give rise to a collective self-avoidance mechanism that yields substantial cooperative speedup without global spatial order. Together, these results show how chemically mediated memory and interactions can optimize collective search across distinct dynamical regimes.