Scale Free Avalanches in Excitatory-Inhibitory Populations of Spiking Neurons with Conductance Based Synaptic Currents
Masud Ehsani and Jürgen Jost
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Submission date: 04. Apr. 2022 (revised version: April 2022)
Keywords and phrases: Critical Brain Hypothesis, Scale Free Avalanches, Linear Poisson Neuron, Bogdanov-Takens Bifurcation
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We investigate spontaneous critical dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate-and-ﬁre neurons with conductance-based synapses. We use a bottom-up approach to derive a single neuron gain function and a linear Poisson neuron approximation which we use to study mean-ﬁeld dynamics of the EI population and its bifurcations. In the low ﬁring rate regime, the quiescent state loses stability due to saddle-node or Hopf bifurcations. In particular, at the Bogdanov-Takens (BT) bifurcation point which is the intersection of the Hopf bifurcation and the saddle-node bifurcation lines of the 2D dynamical system, the network shows avalanche dynamics with power-law avalanche size and duration distributions. This matches the characteristics of low ﬁring spontaneous activity in the cortex. By linearizing gain functions and excitatory and inhibitory nullclines, we can approximate the location of the BT bifurcation point. This point in the control parameter phase space corresponds to the internal balance of excitation and inhibition and a slight excess of external excitatory input to the excitatory population. Due to the tight balance of average excitation and inhibition currents, the ﬁring of the individual cells is ﬂuctuation-driven. Around the BT point, the spiking of neurons is a Poisson process and the population average membrane potential of neurons is approximately at the middle of the operating interval [V Rest,V th]. Moreover, the EI network is close to both oscillatory and active-inactive phase transition regimes.