Suggested further readings

Phase plane analysis

Gerstner, W., Kistler, W. M., Naud, R., and Paninski, L. (2014). Neuronal dynamics: From single neurons to networks and models of cognition, chapter 4 Cambridge University Press. URL:

Firing rate based models

Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical journal 12(1): 1-24. doi: 10.1016/S0006-3495(72)86068-5 Open Access publication.

Balanced amplification

Murphy, B. K., and Miller, K. D. (2009). Balanced amplification: a new mechanism of selective amplification of neural activity patterns. Neuron 61(4): 635-648. doi: 10.1016/j.neuron.2009.02.005 Open Access publication.

Inhibition stabilized networks

Ozeki, H., Finn, I. M., Schaffer, E. S., Miller, K. D., and Ferster, D. (2009). Inhibitory stabilization of the cortical network underlies visual surround suppression. Neuron 62(4): 578-592. doi: 10.1016/j.neuron.2009.03.028 Open Access publication.

Sanzeni, A., Akitake, B., Goldbach, H. C., Leedy, C. E., Brunel, N., and Histed, M. H. (2020). Inhibition stabilization is a widespread property of cortical networks. Elife 9: e54875. doi: 10.7554/eLife.54875 Open Access publication.

Tsodyks, M. V., Skaggs, W. E., Sejnowski, T. J., and McNaughton, B. L. (1997). Paradoxical effects of external modulation of inhibitory interneurons. Journal of neuroscience 17(11): 382-4388. doi: 10.1523/JNEUROSCI.17-11-04382.1997 Open Access publication.

Stabilized supralinear networks

Ahmadian, Y., Rubin, D. B., and Miller, K. D. (2013). Analysis of the stabilized supralinear network. Neural computation 25(8): 1994-2037. doi: 10.1162/NECO_a_00472 Closed Access publication (postprint: Open Access publication) or arxiv:1202.6670.

Ahmadian, Y., and Miller, K. D. (2021). What is the dynamical regime of cerebral cortex?. Neuron 109(21): 3373-3391. doi: 10.1016/j.neuron.2021.07.031 Closed Access publication (preprint: Open Access publication) or arxiv:1908.10101.

Hennequin, G., Ahmadian, Y., Rubin, D. B., Lengyel, M., and Miller, K. D. (2018). The dynamical regime of sensory cortex: stable dynamics around a single stimulus-tuned attractor account for patterns of noise variability. Neuron 98(4): 846-860. doi: 10.1016/j.neuron.2018.04.017 Open Access publication.

Lindsay, G. W., Rubin, D. B., and Miller, K. D. (2019). A simple circuit model of visual cortex explains neural and behavioral aspects of attention. bioRxiv 875534. doi: 10.1101/2019.12.13.875534 Open Access publication.

Rubin, D. B., Van Hooser, S. D., and Miller, K. D. (2015). The stabilized supralinear network: a unifying circuit motif underlying multi-input integration in sensory cortex. Neuron 85(2): 402-417. doi: 10.1016/j.neuron.2014.12.026 Open Access publication.

Network of binary neurons

Van Vreeswijk, C., and Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274(5293): 1724-1726. doi: 10.1126/science.274.5293.1724 Closed Access publication.

Spiking neuronal networks

Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of computational neuroscience, 8(3), 183-208. doi: 10.1023/A:1008925309027 Closed Access publication.

Brunel, N., and Wang, X. J. (2003). What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. Journal of neurophysiology 90(1): 415-430. doi: 10.1152/jn.01095.2002 Closed Access publication.