Abstract
We review a general class of models for self-organized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or "agents," with the tendency to adjust to their "environmental averages." This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, rendezvous in mobile networks, etc. A natural question which arises in this context is to ask when and how clusters emerge through the self-alignment of agents, and what types of "rules of engagement" influence the formation of such clusters. Of particular interest to us are cases in which the self-organized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking of birds, fish, or cells, rendezvous of mobile agents, and, in general, concentration of other traits intrinsic to the dynamics. Many standard models for self-organized dynamics in social, biological, and physical sciences assume that the intensity of alignment increases as agents get closer, reflecting a common tendency to align with those who think or act alike. Moreover, "similarity breeds connection" reflects our intuition that increasing the intensity of alignment as the difference of positions decreases is more likely to lead to a consensus. We argue here that the converse is true: when the dynamics is driven by local interactions, it is more likely to approach a consensus when the interactions among agents increase as a function of their difference in position. Heterophily, the tendency to bond more with those who are different rather than with those who are similar, plays a decisive role in the process of clustering. We point out that the number of clusters in heterophilious dynamics decreases as the heterophily dependence among agents increases. In particular, sufficiently strong heterophilious interactions enhance consensus.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 577-621 |
| Number of pages | 45 |
| Journal | SIAM Review |
| Volume | 56 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2014 |
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Keywords
- Active sets
- Agent-based models
- Clusters
- Connectivity of graphs
- Consensus
- Flocking
- Heterophilious dynamics
- Hydrodynamics
- Kinetic equations
- Mean-field limits
- Self-alignment
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
- Theoretical Computer Science
Cite this
Heterophilious dynamics enhances consensus. / Motsch, Sebastien; Tadmor, Eitan.
In: SIAM Review, Vol. 56, No. 4, 2014, p. 577-621.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Heterophilious dynamics enhances consensus
AU - Motsch, Sebastien
AU - Tadmor, Eitan
PY - 2014
Y1 - 2014
N2 - We review a general class of models for self-organized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or "agents," with the tendency to adjust to their "environmental averages." This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, rendezvous in mobile networks, etc. A natural question which arises in this context is to ask when and how clusters emerge through the self-alignment of agents, and what types of "rules of engagement" influence the formation of such clusters. Of particular interest to us are cases in which the self-organized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking of birds, fish, or cells, rendezvous of mobile agents, and, in general, concentration of other traits intrinsic to the dynamics. Many standard models for self-organized dynamics in social, biological, and physical sciences assume that the intensity of alignment increases as agents get closer, reflecting a common tendency to align with those who think or act alike. Moreover, "similarity breeds connection" reflects our intuition that increasing the intensity of alignment as the difference of positions decreases is more likely to lead to a consensus. We argue here that the converse is true: when the dynamics is driven by local interactions, it is more likely to approach a consensus when the interactions among agents increase as a function of their difference in position. Heterophily, the tendency to bond more with those who are different rather than with those who are similar, plays a decisive role in the process of clustering. We point out that the number of clusters in heterophilious dynamics decreases as the heterophily dependence among agents increases. In particular, sufficiently strong heterophilious interactions enhance consensus.
AB - We review a general class of models for self-organized dynamics based on alignment. The dynamics of such systems is governed solely by interactions among individuals or "agents," with the tendency to adjust to their "environmental averages." This, in turn, leads to the formation of clusters, e.g., colonies of ants, flocks of birds, parties of people, rendezvous in mobile networks, etc. A natural question which arises in this context is to ask when and how clusters emerge through the self-alignment of agents, and what types of "rules of engagement" influence the formation of such clusters. Of particular interest to us are cases in which the self-organized behavior tends to concentrate into one cluster, reflecting a consensus of opinions, flocking of birds, fish, or cells, rendezvous of mobile agents, and, in general, concentration of other traits intrinsic to the dynamics. Many standard models for self-organized dynamics in social, biological, and physical sciences assume that the intensity of alignment increases as agents get closer, reflecting a common tendency to align with those who think or act alike. Moreover, "similarity breeds connection" reflects our intuition that increasing the intensity of alignment as the difference of positions decreases is more likely to lead to a consensus. We argue here that the converse is true: when the dynamics is driven by local interactions, it is more likely to approach a consensus when the interactions among agents increase as a function of their difference in position. Heterophily, the tendency to bond more with those who are different rather than with those who are similar, plays a decisive role in the process of clustering. We point out that the number of clusters in heterophilious dynamics decreases as the heterophily dependence among agents increases. In particular, sufficiently strong heterophilious interactions enhance consensus.
KW - Active sets
KW - Agent-based models
KW - Clusters
KW - Connectivity of graphs
KW - Consensus
KW - Flocking
KW - Heterophilious dynamics
KW - Hydrodynamics
KW - Kinetic equations
KW - Mean-field limits
KW - Self-alignment
UR - http://www.scopus.com/inward/record.url?scp=84908879266&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84908879266&partnerID=8YFLogxK
U2 - 10.1137/120901866
DO - 10.1137/120901866
M3 - Article
AN - SCOPUS:84908879266
VL - 56
SP - 577
EP - 621
JO - SIAM Review
JF - SIAM Review
SN - 0036-1445
IS - 4
ER -