  In this paper, we present and analyse two Hopfield-like nonlinear networks,
in continuous-time and discrete-time respectively. The proposed network is
based on an autonomous linear system with a symmetric weight matrix, which is
designed to be unstable, and a nonlinear function stabilizing the whole network
thanks to a manipulated state variable called``ultimate SIR''. This variable is
observed to be equal to the traditional Signal-to-Interference Ratio (SIR)
definition in telecommunications engineering.
  The underlying linear system of the proposed continuous-time network is
$\dot{{\mathbf x}} = {\mathbf B} {\mathbf x}$ where {\bf B} is a real symmetric
matrix whose diagonal elements are fixed to a constant. The nonlinear function,
on the other hand, is based on the defined system variables called ``SIR''s. We
also show that the ``SIR''s of all the states converge to a constant value,
called ``system-specific Ultimate SIR''; which is equal to
$\frac{r}{\lambda_{max}}$ where $r$ is the diagonal element of matrix ${\bf B}$
and $\lambda_{max}$ is the maximum (positive) eigenvalue of diagonally-zero
matrix $({\bf B} - r{\bf I})$, where ${\bf I}$ denotes the identity matrix. The
same result is obtained in its discrete-time version as well.
  Computer simulations for binary associative memory design problem show the
effectiveness of the proposed network as compared to the traditional Hopfield
Networks.
