  Multistability is one of the most important phenomena in dynamical systems,
e.g. bistability enables the implementation of logic gates and therefore
computation. Recently multistability has attracted a greatly renewed interest
related to memristors and graphene structures. We investigate tristability in
velocity dynamics of a Brownian particle subjected to a tilted periodic
potential. It is demonstrated that the origin of this effect is attributed to
extreme value statistics in the form of arcsine law for the velocity dynamics
at the zero temperature limit. We analyze the impact of thermal fluctuations
and construct the phase diagram for the stability of the velocity dynamics. It
suggests an efficient strategy to control the multistability by changing solely
the force acting on the particle or temperature of the system. Our findings for
the paradigmatic model of nonequilibrium statistical physics apply to, inter
alia, Brownian motors, Josephson junctions, cold atoms dwelling in optical
lattices and colloidal systems.
