Impact of memory on clustering in spontaneous particle aggregation

The effect of short-term and long-term memory on spontaneous aggregation oforganisms is studied using an agent-based stochastic model, where each individual modulates its random movement based on the perceived local density of its neighbours. Memory is introduced via a chain of K internal variables, allowing agents to retain past environmental information. The number of internal variables, K, controls the memory length. The macroscopic Fokker-Planck equation is formally derived in the large-particle limit. To explain the formation and shape of particle clusters, the steady states of the Fokker-Planck equation are characterized, and systematic stochastic simulations of the individual-basedmodel performed. The short-term memory promotes cluster coarsening, while long-term memory disrupts aggregation, increasing the number of outliers and instances with no clustering. Statistical analysis shows that memory inhibits the particles' responsivity to environmental cues, specifically the perceived density of their neighbours, explaining the reduced clustering tendency at higher values of thememory length, K. This study therefore provides an insight into how memory influences emergent spatial patterns in self-organizing systems of organisms.