Social hierarchy is central to decision-making in the coordinated movement of many swarming species. Here we propose a hierarchical swarm model in the spirit of the Vicsek model of self-propelled particles. We show that, as the hierarchy becomes important, the swarming transition changes from the weak first-order transition observed for egalitarian populations, to a stronger first-order transition for intermediately strong hierarchies, and finally the discontinuity reduces until vanish, where the order-disorder transition appears to be absent in the extremely despotic societies. Associated to this we observe that the spatial structure of the swarm, as measured by the correlation between the density and velocity fields, is strongly mediated by the hierarchy. A two-group model and vectorial noise are also studied for verification. Our results point out the particular relevance of the hierarchical structures to swarming transitions when doing specific case studies.
Large-scale cooperation underpins the evolution of ecosystems and the human society, and the collective behaviors by self-organization of multi-agent systems are the key for understanding. As artificial intelligence (AI) prevails in almost all branches of science, it would be of great interest to see what new insights of collective behavior could be obtained from a multi-agent AI system. Here, we introduce a typical reinforcement learning (RL) algorithm -Q learning into evolutionary game dynamics, where agents pursue optimal action on the basis of the introspectiveness rather than the birth-death or imitation processes in the traditional evolutionary game (EG). We investigate the cooperation prevalence numerically for a general 2 × 2 game setting. We find that the cooperation prevalence in the multi-agent AI is amazingly of equal level as in the traditional EG in most cases. However, in the snowdrift games with RL we also reveal that explosive cooperation appears in the form of periodic oscillation, and we study the impact of the payoff structure on its emergence. Finally, we show that the periodic oscillation can also be observed in some other EGs with the RL algorithm, such as the rock-paper-scissors game. Our results offer a reference point to understand emergence of cooperation and oscillatory behaviors in nature and society from AI's perspective.
The spread of infectious diseases, rumors, fashions, and innovations are complex contagion processes, embedded in network and spatial contexts. While the studies in the former context are intensively expanded, the latter remains largely unexplored. In this paper, we investigate the pattern formation of an interacting contagion, where two infections, A and B, interact with each other and diffuse simultaneously in space. The contagion process for each follows the classical susceptible-infected-susceptible kinetics, and their interaction introduces a potential change in the secondary infection propensity compared to the baseline reproduction number R 0 . We show that the nontrivial spatial infection patterns arise when the susceptible individuals move faster than the infected and the interaction between the two infections is neither too competitive nor too cooperative. Interestingly, the system exhibits pattern hysteresis phenomena, i.e., quite different parameter regions for patterns exist in the direction of increasing or decreasing R 0 . Decreasing R 0 reveals remarkable enhancement in contagion prevalence, meaning that the eradication becomes difficult compared to the single-infection or coinfection without space. Linearization analysis supports our observations, and we have identified the required elements and dynamical mechanism, which suggests that these patterns are essentially Turing patterns. Our work thus reveals new complexities in interacting contagions and paves the way for further investigation because of its relevance to both biological and social contexts.
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