  We propose a third order dynamical system for solving a nonlinear equation in
Hilbert spaces where the operator is cocoercive with respect to the solutions
set. Under mild conditions on the parameters, we establish the existence and
uniqueness of the generated trajectories as well as its asymptotic convergence
to a solution of the equation. When the operator is strongly monotone with
respect to the solutions set, we deliver an exponential convergence rate of
$e^{-2t}$, which is significantly faster than the known results of second order
dynamical systems. In particular, for convex optimization problems, the
proposed dynamical system provides a fast convergence rate of {\bf
$\mathcal{O}(\frac{1}{t^3})$} for the objective values. In addition, we discuss
the applications of the proposed dynamical system to several splitting monotone
inclusion problems.
