@inproceedings{fc4d5a0361e34bc995d511012e2df49b,
title = "Bifurcation analysis of a heterogeneous mean-field oscillator game model",
abstract = "This paper studies the phase transition in a heterogeneous mean-field oscillator game model using methods from bifurcation theory. In our earlier paper [1], we had obtained a coupled PDE model using mean-field approximation and described linear analysis of the PDEs that suggested possibility of a Hamiltonian Hopf bifurcation. In this paper, we simplify the analysis somewhat by relating the solutions of the PDE model to the solutions of a certain nonlinear eigenvalue problem. Both analysis and computations are much easier for the nonlinear eigenvalue problem. Apart from the bifurcation analysis that shows existence of a phase transition, we also describe a Lyapunov-Schmidt perturbation method to obtain asymptotic formulae for the small amplitude bifurcated solutions. For comparison, we also depict numerical solutions that are obtained using the continuation software AUTO.",
author = "Huibing Yin and Mehta, {Prashant G.} and Meyn, {Sean P.} and Shanbhag, {Uday V.}",
year = "2011",
doi = "10.1109/CDC.2011.6161203",
language = "English (US)",
isbn = "9781612848006",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "3895--3900",
booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",
address = "United States",
note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",
}