Abstract: Deterministic and stochastic models of Brownian motion in ferrofluids are of interest to
researchers, especially those related to drug delivery systems. The Brownian motion of nanoparticles
in a ferrofluid environment was theoretically analyzed in this research. The state of the art in
clinical drug delivery systems using ferromagnetic particles is briefly presented. The motion of the
nanoparticles in an external field and as a random variable is elaborated by presenting a theoretical
model. We analyzed the theoretical model and performed computer simulation by using Maple
software. We used simple low-dimensional deterministic systems that can exhibit diffusive behavior.
The ferrofluid in the gravitational field without the presence of an external magnetic field in the xy
plane was observed. Control parameter p was mapped as related to the fluid viscosity. Computer
simulation showed that nanoparticles can exhibit deterministic patterns in a chaotic model for certain
values of the control parameter p. Linear motion of the particles was observed for certain values of
the parameter p, and for other values of p, the particles move randomly without any rule. Based on
our numerical simulation, it can be concluded that the motion of nanoparticles could be controlled by
inherent material properties and properties of the surrounding media, meaning that the delivery of
drugs could possibly be executed by a ferrofluid without an exogenous power propulsion strategy.
However, further studies are still needed.