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Balanced neural networks -- in which excitatory and inhibitory inputscompensate each other on average -- give rise to a dynamical phase dominated byfluctuations called asynchronous state, crucial for brain functioning. However,structural disorder -- which is inherent to random networks -- can hinder suchan excitation-inhibition balance. Indeed, structural and synapticheterogeneities can generate extended regions in phase space akin to criticalpoints, called Griffiths phases, with dynamical features very different fromthose of asynchronous states. Here, we study a neural-network model withtunable levels of heterogeneity able to display these two types of dynamicalregimes -- i.e., asynchronous states and Griffiths phases -- putting themtogether within a single phase diagram. Using this simple model, we are able toemphasize the crucial role played by synaptic plasticity and homeostasis tore-establish balance in intrinsically heterogeneous networks.

From asynchronous states to Griffiths phases and back: structural heterogeneity and homeostasis in excitatory-inhibitory networks