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Fig. 8 | The Journal of Mathematical Neuroscience

Fig. 8

From: Symmetries Constrain Dynamics in a Family of Balanced Neural Networks

Fig. 8

Oscillations persist despite randomness in the connectivity matrix. AB Solutions for two different networks of size \(N = 20\): \(g=3\). Here, \(\sqrt{N} \mathbf {G}\equiv \mathbf {H}+ \epsilon \mathbf {A}_{1,2}\). From top to bottom: \(\epsilon^{2} = 1, 2^{-1}, 2^{-2}, 2^{-3}, 2^{-4}, 2^{-5}, 2^{-6}\text{, and }0\). C Solutions for a network of size \(N=200\). The connectivity matrix is given by \(\sqrt{N} \mathbf {G}\equiv \mathbf {H}+ \epsilon \mathbf {A}\) for a single A. From top to bottom: \(\epsilon^{2} = 1, 2^{-1}, 2^{-2}, 2^{-3}, 2^{-4}, 2^{-5}, 2^{-6}\text{, and }0\). D Solutions for a network of size \(N=200\), but where \(\sqrt{N} \mathbf {G}\equiv\epsilon \mathbf {A}\) (i.e. no mean). The random connectivity matrix A is the same as in panel C. In panels AB, the traces of \(n_{E}\) excitatory (blue) and \(n_{I}\) inhibitory (red) neurons are shown. In panels CD, only a subset (twenty E and six I cells) is displayed. E, F Eigenvalues of the connectivity matrices \(\sqrt{N} \mathbf {G}\equiv \mathbf {H}+ \epsilon \mathbf {A}\) (E) and \(\sqrt {N} \mathbf {G}\equiv\epsilon \mathbf {A}\) (F) used in panels C and D, respectively

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