# Transition to chaos in random neuronal networks

arXiv: https://arxiv.org/abs/1508.06486 · HTML: https://mlsanity.com/paper/1508.06486/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2015.

## Built on by (most cited first, 11 of 11)

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- [Curl Descent: Non-Gradient Learning Dynamics with Sign-Diverse Plasticity](https://mlsanity.com/paper/2510.02765/) (2025)
- [A unified theory of feature learning in RNNs and DNNs](https://mlsanity.com/paper/2602.15593/) (2026)
- [KPFlow: An Operator Perspective on Dynamic Collapse Under Gradient Descent Training of Recurrent Networks](https://mlsanity.com/paper/2507.06381/) (2025)
- [Neuronal architecture extracts statistical temporal patterns](https://mlsanity.com/paper/2301.10203/) (2023)
- [Stability of Multi-Agent Learning in Competitive Networks: Delaying the Onset of Chaos](https://mlsanity.com/paper/2312.11943/) (2023)
- [Dynamical stability for dense patterns in attractor neural networks](https://mlsanity.com/paper/2507.10383/) (2025)

## Abstract (arXiv)

Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic dynamics. Indeed, simplified rate-based large neuronal networks with random synaptic connections are known to exhibit sharp transition from fixed point to chaotic dynamics when the synaptic gain is increased. However, the existence of a similar transition in neuronal circuit models with more realistic architectures and firing dynamics has not been established. In this work we investigate rate based dynamics of neuronal circuits composed of several subpopulations and random connectivity. Nonzero connections are either positive-for excitatory neurons, or negative for inhibitory ones, while single neuron output is strictly positive; in line with known constraints in many biological systems. Using Dynamic Mean Field Theory, we find the phase diagram depicting the regimes of stable fixed point, unstable dynamic and chaotic rate fluctuations. We characterize the properties of systems near the chaotic transition and show that dilute excitatory-inhibitory architectures exhibit the same onset to chaos as a network with Gaussian connectivity. Interestingly, the critical properties near transition depend on the shape of the single- neuron input-output transfer function near firing threshold. Finally, we investigate network models with spiking dynamics. When synaptic time constants are slow relative to the mean inverse firing rates, the network undergoes a sharp transition from fast spiking fluctuations and static firing rates to a state with slow chaotic rate fluctuations. When the synaptic time constants are finite, the transition becomes smooth and obeys scaling properties, similar to crossover phenomena in statistical mechanics