Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 266, Issue 12, Pages 8067-8093Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2018.12.025
Keywords
Multi-population Mean-Field Games; Bifurcation; Instability
Categories
Funding
- Fondazione CaRiPaRo Project Nonlinear Partial Differential Equations: Asymptotic Problems and Mean-Field Games
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For non-monotone single and two-populations time-dependent Mean-Field Game systems we obtain the existence of an infinite number of branches of non-trivial solutions. These non-trivial solutions are in particular shown to exhibit an oscillatory behaviour when they are close to the trivial (constant) one. The existence of such branches is derived using local and global bifurcation methods, that rely on the analysis of eigenfunction expansions of solutions to the associated linearized problem. Numerical analysis is performed on two different models to observe the oscillatory behaviour of solutions predicted by bifurcation theory, and to study further properties of branches far away from bifurcation points. (C) 2018 Elsevier Inc. All rights reserved.
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