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Fig. 18 | The Journal of Mathematical Neuroscience

Fig. 18

From: Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

Fig. 18

Spectrum for the phase oscillator continuum model (42) with a mixture of spatial scales and nonlinearities. Here \(H_{1}(\theta)=H_{2}(\theta)=\sin(\theta+ \alpha)\), \(H_{3}=\sin (2\theta + \alpha)\) and \(W_{\mu}(x)=\gamma_{\mu}\exp(-\gamma_{\mu}|x|)/2\) with \(\gamma _{2}=\gamma_{3}\). Parameters are \(\epsilon_{1}=0.5\), \(\epsilon_{2}=0.15\), \(\epsilon_{3}=-0.3\), \(\gamma_{1}=1/2\), \(\gamma_{2}=1/4\), and \(\alpha=-1.45\). There is a band of unstable wave-numbers with \(p\in(0,p_{c})\), with \(p_{c} \simeq1.25\)

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