Figure 1

The illustrative construction of the delay kernel $L\left(\mathbf{x},\tau \right)$. Assuming a spatial kernel (left image), $L$ exhibits rings with radius $c\tau$ (images on the right for different delay times) which is the interaction distance of the system at the delay time $\tau$.Reuse & Permissions

Figure 2

Spatiotemporal response activity to the external stimulus $I\left(\mathbf{x},t\right)=I_0+e^{-{\mathbf{x}}^2/{\sigma }_I^2}$ for the spatial connectivity function $K\left(\mathbf{x}\right)$ by the numerical simulation of Eq. (1). Used (dimensionless) parameters are $K_o=0.1,c=10,l=10,k_c=10\pi /l,\sigma =10,{\sigma }_I=0.2,N=512,$ $\tau =1,\Delta t=0.005$. Moreover, $I_0=2.0$, $S\left[V\right]=2/\left\{1+\text{exp}\left[-5.5\left(V-3\right)\right]\right\}$ and $V_0=2.00083$. The initial values are chosen to $V\left(\mathbf{x},\theta \right)=V_0$ for the delay interval $-l/\sqrt{2}c\le \theta \le 0$. Introducing the temporal and spatial scale $\tau =10\text{ms}$ and $\lambda =1.0\text{mm}$, the results reflect the spatiotemporal activity with transmission speed $c=1.0\text{m}/\text{s}$ and the domain length $l=10\text{mm}$, which are realistic values for layer 2/3 in visual cortex. Then the points $A$ and $B$ are located at a distance $d_A=2.1\text{mm}$ and $d_B=3.8\text{mm}$ from the stimulus onset location at the origin, respectively. The bar in the plots is 0.83 mm long.Reuse & Permissions

Figure 3

(Color online) Transmission delay-induced breathers evoked by an anisotropic external stimulus. The spatial connectivity function is chosen to $K\left(r\right)=10\text{exp}\left(-r/3\right)/\left(18\pi \right)-14\text{exp}\left(-r/7\right)/\left(98\pi \right)$ and the input magnitude and variances are $I_0=10$ and ${\Sigma }_{11}^{-1}=3,{\Sigma }_{22}^{-1}=5$, respectively. Further parameters are $c=100$, $l=30$, $N=512$, $\tau =1$, $\Delta t=0.05$, and $V_{\text{thresh}}=0.005$. The initial values are chosen to $V\left(\mathbf{x},\theta \right)=0$ for the delay interval $-L/\sqrt{2}c\le \theta \le 0$.Reuse & Permissions