Fig. 8

Left: Example of solution on the unperturbed torus \(\mathcal{T}_{0}\) obtained with a Newton algorithm. Right: Numerical solution of (1) projected on the unperturbed torus \(\mathcal{T}_{0}\). The green hexagon is the fundamental domain from Proposition 4.3. The bottom right parallelogram is the result of six simulations, the hexagon was built by tiling this parallelogram. The parameters are as follows: connectivity \(J_{\mathrm{LR}}^{p,a}(\mathbf {x},\mathbf {y})\) (see Appendix B), \(\epsilon_{\mathrm{LR}}=0.5\), \(\chi=0.2\), and \(\sigma=1.11264\). The size of the cortex is \(8\times2\pi\). The numerical mesh size is \(3\cdot1024^{2}\)