How chaotic is the balanced state?
BMC Neuroscience volume 10, Article number: O20 (2009)
Local cortical circuits often exhibit highly irregular spiking dynamics that appears to be random. Such irregular dynamics are commonly considered as a "ground state" of cortical circuits. In a fundamental work, van Vreeswijk and Sompolinsky  suggested that a "chaotic balanced state" underlies this irregular cortical activity. In such a state, strong inhibitory and excitatory inputs to each neuron balance on average and only the fluctuations generate spikes. Moreover, the original high-dimensional network dynamics and a slightly perturbed version of it rapidly diverge from each other, suggesting that chaos is the dynamical mechanism that induces irregularity. Here we show analytically and numerically that irregular balanced activity may equally well be generated by collective dynamics that is not chaotic but stable almost everywhere in state space. This dynamics has the same coarse statistical features as its chaotic counterpart (see figure 1). Our results reveal that chaos is not necessary to generate irregular balanced activity in an entire class of deterministic spiking neural networks. Most importantly, the results also indicate that not chaos or stochasticity, but some other dynamical mechanism may actually underlie the irregularity observed in cortical activity.
van Vreeswijk C, Sompolinsky H: Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science. 1996, 274: 1724-1726. 10.1126/science.274.5293.1724.
Jahnke S, Memmesheimer RM, Timme M: Stable irregular dynamics in complex neural networks. Phys Rev Lett. 2008, 100: 048102-10.1103/PhysRevLett.100.048102.
We thank the Federal Ministry of Education and Research (BMBF) for partial support under Grant No. 01GQ430. RMM further thanks the Sloan Swartz Foundation for partial support.
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Jahnke, S., Memmesheimer, R. & Timme, M. How chaotic is the balanced state?. BMC Neurosci 10 (Suppl 1), O20 (2009). https://doi.org/10.1186/1471-2202-10-S1-O20