Collective behaviors of animal groups may stem from visual lateralization-Tending to obtain information through one eye.

Animal groups exhibit various captivating movement patterns, which manifest as intricate interactions among group members. Several models have been proposed to elucidate collective behaviors in animal groups. These models achieve a certain degree of efficacy; however, inconsistent experimental findings suggest insufficient accuracy. Experiments have shown that some organisms employ a single information channel and visual lateralization to glean knowledge from other individuals in collective movements. In this study, we consider individuals' visual lateralization and a single information channel and develop a self-propelled particle model to describe the collective behavior of large groups. The results suggest that homogeneous visual lateralization gives the group a strong sense of cohesiveness, thereby enabling diverse collective behaviors. As the overlapping field grows, the cohesiveness gradually dissipates. Inconsistent visual lateralization among group members can reduce the cohesiveness of the group, and when there is a high degree of heterogeneity in visual lateralization, the group loses their cohesiveness. This study also examines the influence of visual lateralization heterogeneity on specific formations, and the results indicate that the directional migration formation is responsive to such heterogeneity. We propose an information network to portray the transmission of information within groups, which explains the cohesiveness of groups and the sensitivity of the directional migration formation.

Structural position vectors and symmetries in complex networks.

Symmetries, due to their fundamental importance to dynamical processes on networks, have attracted a great deal of current research. Finding all symmetric nodes in large complex networks typically relies on automorphism groups from algebraic-group theory, which are solvable in quasipolynomial time. We articulate a conceptually appealing and computationally extremely efficient approach to finding and characterizing all symmetric nodes by introducing a structural position vector (SPV) for each node in networks. We establish the mathematical result that symmetric nodes must have the same SPV value and demonstrate, using six representative complex networks from the real world, that all symmetric nodes in these networks can be found in linear time. Furthermore, the SPVs not only characterize the similarity of nodes but also quantify the nodal influences in propagation dynamics. A caveat is that the proved mathematical result relating the SPV values to nodal symmetries is not sufficient; i.e., nodes having the same SPV values may not be symmetric, which arises in regular networks or networks with a dominant regular component. We point out with an analysis that this caveat is, in fact, shared by the known existing approaches to finding symmetric nodes in the literature. We further argue, with the aid of a mathematical analysis, that our SPV method is generally effective for finding the symmetric nodes in real-world networks that typically do not have a dominant regular component. Our SPV-based framework, therefore, provides a physically intuitive and computationally efficient way to uncover, understand, and exploit symmetric structures in complex networks arising from real-world applications.

Metamorphoses and explosively remote synchronization in dynamical networks.

We uncover a phenomenon in coupled nonlinear networks with a symmetry: as a bifurcation parameter changes through a critical value, synchronization among a subset of nodes can deteriorate abruptly, and, simultaneously, perfect synchronization emerges suddenly among a different subset of nodes that are not directly connected. This is a synchronization metamorphosis leading to an explosive transition to remote synchronization. The finding demonstrates that an explosive onset of synchrony and remote synchronization, two phenomena that have been studied separately, can arise in the same system due to symmetry, providing another proof that the interplay between nonlinear dynamics and symmetry can lead to a surprising phenomenon in physical systems.