Fig. 4

Example of dynamics for the PO map in Fig. 2(a) in the case where \(\varGamma= \langle \mathbf {R}_{s},\mathbf {T}_{0,2\pi} \rangle\) and \(\theta_{0}=0\). Left: Sketch of the phase portrait in the fundamental domain. Right: Eight numerical trajectories of (1) projected on the unperturbed torus \(\mathcal{T}_{0}\). The fundamental domain is superimposed to compare with prediction. The parameters are as follows: connectivity \(J_{\mathrm{LR}}^{p,r}(\mathbf {x},\mathbf {y})\) (see Appendix B), \(\epsilon_{\mathrm{LR}}=0.001\), \(\chi=0.9\), and \(\sigma=1.06264\). The size of the cortex is \(4\times2\pi\). The numerical mesh size is 1024²