640 research outputs found
Asymptotic behavior of gradient-like dynamical systems involving inertia and multiscale aspects
In a Hilbert space , we study the asymptotic behaviour, as time
variable goes to , of nonautonomous gradient-like dynamical
systems involving inertia and multiscale features.
Given a general Hilbert space, and two convex
differentiable functions, a positive damping parameter, and a function of which tends to zero as goes to , we
consider the second-order differential equation This
system models the emergence of various collective behaviors in game theory, as
well as the asymptotic control of coupled nonlinear oscillators. Assuming that
tends to zero moderately slowly as goes to infinity, we show
that the trajectories converge weakly in . The limiting equilibria
are solutions of the hierarchical minimization problem which consists in
minimizing over the set of minimizers of . As key assumptions,
we suppose that and that, for
every belonging to a convex cone depending on the data
and where is
the Fenchel conjugate of , and is the support function of
. An application is given to coupled oscillators
Asymptotic behavior of coupled dynamical systems with multiscale aspects
We study the asymptotic behavior, as time t goes to infinity, of
nonautonomous dynamical systems involving multiscale features. These systems
model the emergence of various collective behaviors in game theory, as well as
the asymptotic control of coupled sytems.Comment: 20 page
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