Limit cycles in replicator-mutator network dynamics
- 1 December 2011
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 3922-3927
- https://doi.org/10.1109/cdc.2011.6160995
Abstract
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.Keywords
This publication has 17 references indexed in Scilit:
- Evolutionary dynamics, intrinsic noise, and cycles of cooperationPhysical Review E, 2010
- Evolutionary bandwidth allocation and routing in large-scale wireless sensor networksPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2010
- Eavesdropping and language dynamicsJournal of Theoretical Biology, 2010
- An individual-based evolutionary dynamics model for networked social behaviorsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2009
- Evolutionary dynamics of behavior in social networksPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2007
- Coevolutionary dynamics in large, but finite populationsPhysical Review E, 2006
- Chaos and languageProceedings Of The Royal Society B-Biological Sciences, 2004
- Bifurcation analysis of the fully symmetric language dynamical equationJournal of Mathematical Biology, 2003
- The Evolutionary Dynamics of Grammar AcquisitionJournal of Theoretical Biology, 2001
- Evolutionary Games and Population DynamicsPublished by Cambridge University Press (CUP) ,1998