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: neuronaldynamics.epfl.ch/online/Ch4.html

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 .

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 .

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 .

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 .

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 .

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 (postprint: europepmc.org/articles/pmc4026108 ) 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 (preprint: arxiv.org/pdf/1908.10101 ) 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 .

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 .

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 .

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 .

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 .

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 .