SLpsolCE\]) and determined by its position on the circle. More specifically, the plane waves with the higher amplitude tend to be more stable than those with the lower amplitude. Figure \[fig:SLBD\] illustrates this by showing stable, as well as weakly and strongly unstable “positions” on the circle. Thus, with the increasing $\alpha$, the number of stable plane waves increases. Plane waves with smaller $\left|k_{-}\right|$ also tend to be more stable than those with larger $\left|k_{-}\right|$. Therefore we expect that the plane waves which are almost diagonal are more abundantly observed.

FitzHugh-Nagumo neurons with homogeneous coupling delays\[sec:FHN-hom\]
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In this section we consider a lattice of $M\times N$ delay-coupled FitzHugh-Nagumo neurons, which are coupled via excitatory chemical synapses. The coupling architecture is the same as described in section \[sec: model system\]. The model system reads $$\begin{aligned}
  \label{eq:FHN}
\begin{aligned}
\frac{\mathrm{d}}{\mathrm{d}t}v_{m,n} &= v_{m,n}-\frac{1}{3}v_{m,n}^{3}-w_{m,n}+I+\\
&\quad +\frac{C}{2}(v_{r}-v_{m,n})(s_{m-1,n}(t-\tau)+s_{m,n-1}(t-\tau))\\
\frac{\mathrm{d}}{\mathrm{d}t}w_{m,n} &= \varepsilon(v_{m,n}+a-bw_{m,n})\\
\frac{\mathrm{d}}{\mathrm{d}t}s_{m,n} &= \alpha(v_{m,n})(1-s_{m,n})-0.6s_{m,n}
\end{aligned}\end{aligned}$$ with $\alpha(v)=\frac{1}{2}[1+e^{-5(v-1)}]^{-1}$. The variable $v_{m,n}$ denotes the membrane potential of the corresponding neuron and $w_{m,n}$ is a recovery variable, combining several microscopic dynamical variables of the biological neuron. The external stimulus current applied to the neuron is denoted by $I$ and $C$ is the coupling strength. We fix the parameters $a=0.7$, 