# A theory for self-sustained balanced states in absence of strong external currents

## TL;DR

This paper proposes a new mechanism for maintaining balanced neural activity in the brain using short-term synaptic depression, eliminating the need for strong external inputs.

## Contribution

The study introduces a biologically plausible mechanism for self-sustained balanced neural activity via short-term synaptic depression without strong external currents.

## Key findings

- Short-term synaptic depression dynamically balances network activity without strong external driving.
- Rate Chaos emerges in densely connected networks with strong synaptic strength.
- The transition to chaos depends on network structure and shrinks as network size increases.

## Abstract

Recurrent neural networks with balanced excitation and inhibition exhibit irregular asynchronous dynamics, which is fundamental for cortical computations. Classical balance mechanisms require strong external input currents in order to sustain finite firing rates, thus raising concerns about their biological plausibility. Here, we investigate an alternative mechanism based on short-term synaptic depression (STD) acting on excitatory-excitatory synapses, which dynamically balances the network activity without the need of strong external driving. Using accurate numerical simulations and theoretical investigations we characterize the dynamics of a densely connected recurrent network made up of N rate-neuron models encompassing STD. Depending on the synaptic strength J0, the network exhibits two distinct regimes: at sufficiently small J0, it converges to a homogeneous fixed point, while for sufficiently large J0
Rate Chaos emerges. For finite networks, we observe a transition region at intermediate J0, where the system passes from the homogeneous fixed point to Rate Chaos following several different routes to chaos depending on the network realization. Furthermore, we show that the width of the transition region shrinks for increasing N and eventually vanishes in the thermodynamic limit (N→∞). The characterization of the Rate Chaos regime has been performed by means of Dynamical Mean Field (DMF) approaches. This analysis has revealed on one side that the novel balancing mechanism is able to sustain finite irregular activity even in the thermodynamic limit, and on the other side that balancing occurs via dynamic cancellation of the correlations in the synaptic input currents induced by the dense connectivity. Our findings show that STD provides an intrinsic self-regulating mechanism for balanced networks, sustaining irregular yet stable activity without the need of biologically unrealistic strong external currents. This work extends the balanced network paradigm, offering insights into how cortical circuits could maintain robust dynamics via synaptic adaptation.

The human brain is constantly active. This ongoing activity is not random but follows complex patterns that emerge from the interactions between billions of neurons. Understanding how these patterns arise is a fundamental question in neuroscience. One influential idea is that the brain maintains a delicate balance between excitatory and inhibitory signals, preventing runaway activity while allowing rich, flexible dynamics. However, classic theories for this balance mechanism often require strong external inputs to sustain realistic firing rates, which may not agree with biological observations.

Early theoretical work on self-sustained activity in large neuronal networks emphasized the role of intrinsically active neurons as a necessary ingredient to sustain low-rate firing in isolated systems [1]. In contrast, we propose an alternative mechanism based on a biological process called short-term synaptic depression. This process weakens excitatory-excitatory connections when neurons fire too fast, acting as a natural self-regulating mechanism. Using mathematical analysis and computer simulations, we show that this mechanism can maintain stable irregular activity, similar to that observed in the cortex, without the need of strong external inputs. Furthermore, we identify several different paths that our model follows to pass from stable activity to chaotic dynamics, somehow resembling the complex scenarios observed in the brain. Our findings suggest that internal synaptic adaptation may play a key role in shaping neural activity, offering new perspectives on how the brain organizes its complex dynamics.