TY - GEN
T1 - Limit cycles in replicator-mutator network dynamics
AU - Pais, Darren
AU - Leonard, Naomi Ehrich
PY - 2011
Y1 - 2011
N2 - The replicator-mutator equations from evolutionary dynamics serve as a model for the evolution of language, behavioral dynamics in social networks, and decision-making dynamics in networked multi-agent systems. Analysis of the stable equilibria of these dynamics has been a focus in the literature, where symmetry in fitness functions is typically assumed. We explore asymmetry in fitness and show that the replicator-mutator equations exhibit Hopf bifurcations and limit cycles. We prove conditions for the existence of stable limit cycles for the dynamics in the case of circulant fitness matrices, and illustrate their existence in the noncirculant case. For decision-making networks, these limit cycles correspond to sustained oscillations in decisions across the group.
AB - The replicator-mutator equations from evolutionary dynamics serve as a model for the evolution of language, behavioral dynamics in social networks, and decision-making dynamics in networked multi-agent systems. Analysis of the stable equilibria of these dynamics has been a focus in the literature, where symmetry in fitness functions is typically assumed. We explore asymmetry in fitness and show that the replicator-mutator equations exhibit Hopf bifurcations and limit cycles. We prove conditions for the existence of stable limit cycles for the dynamics in the case of circulant fitness matrices, and illustrate their existence in the noncirculant case. For decision-making networks, these limit cycles correspond to sustained oscillations in decisions across the group.
UR - http://www.scopus.com/inward/record.url?scp=84860675792&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84860675792&partnerID=8YFLogxK
U2 - 10.1109/CDC.2011.6160995
DO - 10.1109/CDC.2011.6160995
M3 - Conference contribution
AN - SCOPUS:84860675792
SN - 9781612848006
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3922
EP - 3927
BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Y2 - 12 December 2011 through 15 December 2011
ER -