Title:

Advantage of Diversity in Network Dynamics: Convergence Because of (not Despite) Differences

Speaker:

Adilson Motter - Charles E. and Emma H. Morrison Professor, Department of Physics and Astronomy, Northwestern University

Talk Abstract:

Common wisdom assumes that individual entities are more likely to exhibit the same or similar behavior if they are equal to each other—imagine animals using the same gait, lasers pulsing together, birds singing the same notes, and agents reaching consensus. In this presentation, I will show that this assumption is in fact false in networks of interacting entities. This surprising observation is rooted in a new network phenomenon we term “asymmetry-induced symmetry– (AIS), in which the state of the system can be symmetric only when the system itself is not. Using spontaneous synchronization as a model process, I will discuss scenarios where the state in which all nodes exhibit identical dynamics (a state of maximum symmetry) can only be realized when the nodes themselves are not identical. AIS can be seen as the converse of the well-studied phenomenon of symmetry breaking, where the state has less symmetry than the system. AIS has far-reaching implications for processes that involve converging to uniform states; in particular, it offers a mechanism for yet-to-be-explained convergent forms of pattern formation, in which an asymmetric structure develops into a symmetric one. AIS also has implications for consensus dynamics, where it gives rise to scenarios in which interacting agents only reach consensus when they are sufficiently different from each other.

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