Bifurcation analysis of a heterogeneous mean-field oscillator game model

Huibing Yin, Prashant G. Mehta, Sean P. Meyn, Vinayak V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages3895-3900
Number of pages6
DOIs
StatePublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

Fingerprint

Bifurcation Analysis
Mean Field
Nonlinear Eigenvalue Problem
Game
Phase Transition
Lyapunov-Schmidt Method
Phase transitions
Hamiltonians
Hopf bifurcation
Bifurcation Theory
Mean-field Approximation
Perturbation Method
Asymptotic Formula
Hopf Bifurcation
Continuation
Simplify
Numerical Solution
Model
Software

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Yin, H., Mehta, P. G., Meyn, S. P., & Shanbhag, V. V. (2011). Bifurcation analysis of a heterogeneous mean-field oscillator game model. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 3895-3900). [6161203] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2011.6161203
Yin, Huibing ; Mehta, Prashant G. ; Meyn, Sean P. ; Shanbhag, Vinayak V. / Bifurcation analysis of a heterogeneous mean-field oscillator game model. 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. pp. 3895-3900 (Proceedings of the IEEE Conference on Decision and Control).
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Yin, H, Mehta, PG, Meyn, SP & Shanbhag, VV 2011, Bifurcation analysis of a heterogeneous mean-field oscillator game model. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6161203, Proceedings of the IEEE Conference on Decision and Control, pp. 3895-3900, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161203

Bifurcation analysis of a heterogeneous mean-field oscillator game model. / Yin, Huibing; Mehta, Prashant G.; Meyn, Sean P.; Shanbhag, Vinayak V.

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 3895-3900 6161203 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Yin H, Mehta PG, Meyn SP, Shanbhag VV. Bifurcation analysis of a heterogeneous mean-field oscillator game model. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 3895-3900. 6161203. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2011.6161203