Fig. 3

Emergence of Turing–Hopf mixed-mode oscillations in 1-D Wilson–Cowan cortex. (a) Steady state distribution with a selected point at \(P=2\mbox{ mV}\) indicated by green circle. The system has a Hopf instability here. (b) Dispersion curve with synaptic range constant set to ${\sigma }_{EI,IE}=112\text{ μm}$ (see Table 1 for other parameter values) predicts a Turing instability at spatial frequency \(q\simeq2.62\mbox{ waves/mm}\) and a temporal instability of frequency \(f\simeq47\mbox{ Hz}\) (see the \(\omega/2\pi\) value at \(q=0\) axis on dispersion curve). (c) Bird’s-eye view and (d) 3-D spatio-temporal graphs demonstrate spatio-temporal evolution of 1-D network and emergence of mixed-mode Turing–Hopf oscillations in space and time