  In this work it has been developed a new approach to study the stability of a
system composed by an ELKO field interacting with dark matter, which could give
some contribution in order to alleviate the cosmic coincidence problem. It is
assumed that the potential which characterizes the ELKO field is not specified,
but it is related to a constant parameter $\delta$. The strength of the
interaction between matter and ELKO field is characterized by a constant
parameter $\beta$ and it is also assumed that both ELKO field as matter energy
density are related to their pressures by equations of state parameters
$\omega_\phi$ and $\omega_m$, respectively. The system of equations is analysed
by a dynamical system approach. It has been found the conditions of stability
between the parameters $\delta$ and $\beta$ in order to have stable fixed
points for the system for different values of the equation of state parameters
$\omega_\phi$ and $\omega_m$, and the results are presented in form of tables.
The possibility of decay of ELKO field into dark matter or vice versa can be
read directly from the tables, since the parameters $\delta$ and $\beta$
satisfy some inequalities. It allows us to constrain the potential assuming
that we have a stable system for different interactions terms between the ELKO
field and dark matter. The cosmic coincidence problem can be alleviated for
some specific relations between the parameters of the model.
