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.

On the existence of oscillating solutions in non-monotone Mean-Field Games / Cirant, Marco. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 266:12(2019), pp. 8067-8093. [10.1016/j.jde.2018.12.025]

On the existence of oscillating solutions in non-monotone Mean-Field Games

Cirant, Marco
2019-01-01

Abstract

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.
2019
On the existence of oscillating solutions in non-monotone Mean-Field Games / Cirant, Marco. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 266:12(2019), pp. 8067-8093. [10.1016/j.jde.2018.12.025]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2857647
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