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\section{Supporting Information}
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The fixed point equations for the deterministic system without
external inputs by substituting ($ I=0, \sigma=0$) are obtained from
equations \ref{fdt}
\begin{eqnarray}
\label{fdta} 0 &=& -V+\mu U w_TR(V) \nonumber \\
& & \nonumber\\ 0 &=& \frac{1-\mu}{t_r} -U\mu R(V).
\end{eqnarray}
Using the second equation, $\mu$ is expressed by $\mu =
\frac{1}{1+Ut_rR(V)}$ which, together with the first equation,
results in an equation for V only:
\begin{eqnarray}\label{fdtp}
V &=& \frac{Uw_T R(V)}{1+Ut_rR(V)}
\end{eqnarray}
$V=0$ is always a solution of equation \ref{fdtp}, it is denoted by
$V_1$. For $V>T$, equation \ref{fdtp} is in fact a quadratic
equation. There are two additional solutions $V_2$ and $V_3$ that
exist for $w_T$ bigger than a minimal value $w_m$ given by
\begin{eqnarray}
w_m =\frac{(1+\sqrt{Ut_rT})^2}{U}.
\end{eqnarray}
The corresponding value for the voltage is
\begin{eqnarray}
V_m =T+\sqrt{\frac{T}{Ut_r}}.
\end{eqnarray}
The coordinates of the fixed points are $P_2=(V_2, \mu_2)$ and
$P_3=(V_3, \mu_3)$ where $\mu$ is computed as a function of V
according to the equation above (see figure 1).
To analyze the stability of these fixed points, deterministic
dynamical system obtained from equations \ref{fdtp} has to be
linearized around them and one has to compute the eigenvalues of the
associate matrix. A fixed point is stable if the eigenvalues of the
matrix have negative real part. The fixed point $P_3$ is always a
saddle point which is in fact unstable. However, depending on the
value of $w_T$, the fixed point $P_2$ can either be stable or
unstable (repulser). There exits a critical value $w_c$ such that
for $w_m\leq w \leq w_c$, $P_2$ is unstable and for $w \geq w_c$, it
is stable. The transition at the value $w_c$ is a classical Hopf
bifurcation. The value for $w_c$ can be computed numerically for
any set of parameters by digitalizing the matrix of the linearized
dynamical system. In our case,
$w_c \approx 10.3$.
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