Entangled time in flocking: Multi-time-scale interaction reveals emergence of inherent noise

Abstract

Collective behaviors that seem highly ordered and result in collective alignment, such as schooling by fish and flocking by birds, arise from seamless shuffling (such as super-diffusion) and bustling inside groups (such as Lévy walks). However, such noisy behavior inside groups appears to preclude the collective behavior: intuitively, we expect that noisy behavior would lead to the group being destabilized and broken into small sub groups, and high alignment seems to preclude shuffling of neighbors. Although statistical modeling approaches with extrinsic noise, such as the maximum entropy approach, have provided some reasonable descriptions, they ignore the cognitive perspective of the individuals. In this paper, we try to explain how the group tendency, that is, high alignment, and highly noisy individual behavior can coexist in a single framework. The key aspect of our approach is multi-time-scale interaction emerging from the existence of an interaction radius that reflects short-term and long-term predictions. This multi-time-scale interaction is a natural extension of the attraction and alignment concept in many flocking models. When we apply this method in a two-dimensional model, various flocking behaviors, such as swarming, milling, and schooling, emerge. The approach also explains the appearance of super-diffusion, the Lévy walk in groups, and local equilibria. At the end of this paper, we discuss future developments, including extending our model to three dimensions.

New Classification of Collective Animal Behaviour as an Autonomous System

“…Instead, we can confirm the existence of various tipping points in collective behaviour, supporting our hypothesis of living systems evolving to raise Φ. We have already seen one of tipping points as discontinuity between schools of different sizes in this and previous studies [29].…”

“…Self-organised criticality (SOC) is a valuable concept for interpreting complex collective behaviours. Flexibility and robustness can be achieved collectively when the group is in the intermediate state between order and disorder [24][25][26][27][28][29]. For instance, external perturbations of collective systems in SOC models optimise the effective correlation range of each individual to accomplish efficient information transfer [13][14][15][16].…”

Four-Types of IIT-Induced Group Integrity of Plecoglossus altivelis

“…Third, many recent studies have indicated a relationship between integrated information and critical phenomena [ 51 , 66 , 86 , 87 , 88 ]. In addition, the fish school of Plecoglossus altiveliss are known to be in a critical state [ 35 ]. Accordingly, we have a strong motivation to elucidate the type of information exchange between individual using parameters with high values.…”

“…The complexity is characterised using statistical models and information theory. Self-organised criticality (SOC) [ 30 ] is considered a convenient strategy that is evolutionarily adopted by living systems to efficiently cope with their external environment [ 31 , 32 , 33 , 34 , 35 ]. However, for smaller system sizes, heterogeneous interactions [ 36 , 37 ] result in different global motion patterns in and [ 38 , 39 ].…”

New Classification of Collective Animal Behaviour as an Autonomous System

“…The complexity is characterised using statistical models and information theory. Self-organised criticality (SOC) [30] is considered as a convenient strategy that is evolutionarily adopted by living systems to efficiently cope with the external environment [31][32][33][34][35]. However, for smaller system sizes, heterogeneous interactions [36,37] result in different global motion patterns in N = 2 and N = 3 [38,39].…”