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Fig. 11 | The Journal of Mathematical Neuroscience

Fig. 11

From: Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

Fig. 11

Isochrons found using the method of Fourier averages for the Stuart–Landau oscillator: \(\mathrm{d}{z} / \mathrm{d}t =z[\lambda(1+ic)/2+i \omega] - z \vert z\vert ^{2} (1+i c)/2\), \(z=x+iy\), with \(\lambda=2\), \(c=1\) and \(\omega=1\) so that \(T=2\pi\); see [185]. The black curve represents the periodic orbit of the system; in this case, we have \(\theta =\vartheta\). The background colour represents the Fourier average, whilst the coloured lines are the isochrons, given as level sets of the Fourier average. The white dots are the actual isochrons, computed analytically as \((x,y)=((1+r) \cos(\theta+ c \ln(1+r)),(1+r) \sin(\theta+ c \ln (1+r)))\), \(r \in(-1,\infty)\)

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