Criticality and Transmission of Information in a Swarm of Cooperative Units

Abstract

We show that the intelligence of a swarm of cooperative units (birds) emerges at criticality, as an effect of the joint action of frequent organizational collapses and of spatial correlation as extended as the flock size. The organizational collapses make the birds become independent of one another, thereby allowing the flock to follow the direction of the lookout birds. Long-range correlation violates the principle of locality, making the lookout birds transmit information on either danger or resources with a time delay determined by the time distance between two consecutive collapses. DOI: 10.1103/PhysRevLett.107.078103 PACS numbers: 87.23.Cc, 64.60.fd, 89.70.Àa, 89.75.Hc In the recent few years, there has been intense activity to explain why a swarm of birds behaves as a single individual [1,2]. How is it possible that when a predator comes, the swarm changes direction to escape from danger? How is it possible that a subset of a swarm becoming aware of the right direction toward a resource [3] convinces the whole flock to pursue that specific course? In which sense, using a metaphor made popular by Couzin [4], can we interpret the swarm as a cognitive mind?The main purpose of this Letter is to prove that this form of intelligence is the effect of the joint action of frequent organizational collapses, allowing the single birds to recover independence of the others, and of a correlation length as extended as the flock size. Although the environment perceiving units are a small fraction of the total number of units, they exert a determinant action on the swarm during the short rearrangement phase after an organizational collapse, which makes each unit free to select a new direction. This freewill condition allows the swarm to select the new flying directions that are transmitted to all the units by the few danger-or resource-perceiving birds, thanks to the criticality-induced long-range correlation. The connection between dynamic instability and information transfer has been recently observed in locust nymphs [3]. The results of this Letter confirm the importance of this observation, establishing at the same time that the information transfer is made possible by the nonlocal nature of the criticality condition, with a time delay depending on the time distance between two consecutive organizational collapses. The correlation length between birds becomes as extended as the finite swarm size, thereby allowing the lookout birds to transmit their flying direction to the whole swarm. Thus, the mean value hi, proportional to the correlation length, remains finite.To afford a convincing proof that the swarm's intelligence is determined by the joint action of organizational collapses and criticality-induced nonlocality, we proceed in two main steps. In the first step we use a model of bird organization, referred to in this Letter as the bird model, to illustrate the concept of temporal complexity. The second step is based on a simpler model, where the relative positions of the birds are fixed and they have only to ch...

Cooperation in neural systems: Bridging complexity and periodicity

“…It is important to notice that the ML function revealed by the numerical analysis of this article exactly matches the ATA results [29]. This is strong evidence that cooperation generates long-range interactions, thereby making the local-interaction network identical to the ATA network, if a larger K is adopted: Cooperation-induced criticality breaks the local nature of the model [22]. The low-density (N = 100) corresponding waiting time distribution [ Fig.…”

“…[43][44][45]. If this interpretation is correct, the Dragon Kings would be a manifestation of the same cooperation-induced long-range correlation as that proved to be essential for the function of complex systems [22]. The authors of the earlier work of Ref.…”

“…In other words, we prove that cooperation generates longrange interactions, a property proved to be essential for the function of a swarm [22], and with a conveniently large K even the perfect synchronization of Ref. [33].…”

“…As in Refs. [22,23], criticality breaks the statistical independence of two neurons, regardless of their Euclidean distance, For larger values of the cooperation parameter, this eventually yields perfect synchronization and periodicity.…”

“…The hypothesis of criticality affords an attractive way of explaining the intelligent global behavior of cooperative systems. The conversion of local into long-range interactions generated by criticality, termed cooperation-induced long-range interaction, was recently proved to yield an efficient way to transport information [22] and may be used to explain the zero time lag synchronization among remote cerebral cortical areas [23].…”