Collective chemotactic search

Abstract

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.

Figures (11)

• Figure 1: Simulation snapshots of the lattice auto-chemotactic model illustrating the weak- and strong-memory regimes. (left) Weak-memory regime ($D_c=2.5$, $\alpha_c=0.1$, $2\sqrt{D_c\alpha_c}=1$), where the chemical field is short-lived and does not form persistent trails. (right) Strong-memory regime ($D_c=0.01$, $\alpha_c=0.001$, $2\sqrt{D_c\alpha_c}=0.0063$), where persistent, asymmetric trails form along past trajectories and overlap with those of other walkers. In both panels, $N=20$ walkers move in a box of size $L=100$ ($\varphi=0.002$) with coupling strength $\beta=10$. The background color encodes the chemical concentration field and the red circles indicate walker positions.
• Figure 2: Single-agent search as a function of effective persistence length $l_p^\mathrm{eff}$. Mean first-passage time (MFPT) $\bar{T}_1$ versus $l_p^\mathrm{eff}$ in (a) the lattice model, where $l_p^\mathrm{eff}$ is tuned by coupling strength $\beta$, and (b) the off-lattice model, where $l_p^\mathrm{eff}$ is tuned by chemical diffusivity $D_c$. Insets show how $l_p^\mathrm{eff}$ depends on the respective control parameter. For finite chemical decay, the data collapse onto a common master curve consistent with ABP behavior. Empty symbols in (b) correspond to $\alpha_c = 0$, where strong-memory effects lead to systematic deviations from the master curve. In all cases with finite chemical decay, the parameters lie in the finite-memory regime defined in Sec. \ref{['sec:regimes']}, where no persistent trail accumulation occurs.
• Figure 3: (a) Effective persistence length $l_p^{\mathrm{eff}}$ of interacting walkers (circles) compared to the single-particle value (dots) as a function of chemotactic coupling $\beta$. Collisions suppress the growth of $l_p^{\mathrm{eff}}$ at strong coupling. (b) Spatial order parameter $\eta_\mathcal{A}$. (c) Collective MFPT $\bar{T}_N$ (circles) and the independent-search reference $\bar{T}_N^{\mathrm{ind}}$ (dots). (d) Cooperative speedup $\gamma_N$. Parameters: bare persistence $l_p=4/3$ and searcher occupation fraction $\varphi=0.012$.
• Figure 4: Minimum MFPT $\min_{\beta,l_p}(\bar{T}_N\varphi)$ as a function of density $\varphi$ in the lattice model. The corresponding optimal $l_p^\mathrm{eff}$ and $\eta_\mathcal{A}$ are shown. Here $l_p^\infty$ denotes the effective persistence length in the strong-coupling limit $\beta\to\infty$. Shaded regions indicate distinct density regimes with different optimal search strategies.
• Figure 5: Cooperative search speedup $\gamma_N$ versus spatial order $\eta_\mathcal{A}$ for three different models: repulsive Yukawa active Brownian particles (ABPs), auto-chemotactic ABPs, and auto-chemotactic random walkers (RWs). Across all models, increasing spatial order is associated with an enhanced cooperative search speedup (gray shaded region). Color encodes the effective persistence length $l_p^\mathrm{eff}$ of interacting searchers. The lattice occupation fraction is $\varphi=0.012$ and the off-lattice packing fraction $\phi=0.01$.