= Mutually excitatory saturating rate network
{title2=$\tau\dot x=-x+g(y),\quad g(z)=ma^2z^2/(\sigma^2+a^2z^2)$}
The symmetric two-neuron rate model has nonnegative activity and saturating recurrent input. Every equilibrium has $x=y$: otherwise monotonicity of $g$ gives a contradiction. With positive parameters it has three distinct equilibria exactly when $am>2\sigma$, namely zero and $z_\pm=(m\pm\sqrt{m^2-4\sigma^2/a^2})/2$. The lower positive equilibrium is a saddle and the origin and upper equilibrium are stable nodes. The resulting two attracting activity levels model a persistent switch rather than a spiking waveform.
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