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arXiv · 2606.30366

Mean-field theory of rich oscillatory dynamics in low-rank recurrent networks with activity-dependent adaptation

Bowen W. Zheng·Earl K. Miller·Ila R. Fiete
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Abstract

We develop a dynamical mean-field theory for random recurrent networks with low-rank structure and firing-rate-driven adaptation. When the random connectivity is strong enough to generate chaos, increasing adaptation strength drives the network through four regimes: a static coherent state, noise-sustained oscillations that progress from regular to irregular, stochastic switching between symmetric wells, and a global limit cycle. The theory identifies two instability mechanisms, chaos onset from the random connectivity and a Hopf bifurcation of the coherent mode, and shows how adaptation shapes both through the frequency-dependent single-neuron transfer function. A reduced three-dimensional model captures the bifurcation structure of the full network. Above the chaos threshold, coherent population-level oscillations coexist with heterogeneous firing rates and network-generated stochasticity at the single-neuron level. The interaction of adaptation with random and low-rank connectivity produces a rich oscillatory repertoire, including waxing-and-waning rhythmic episodes, persistent state switching, and slow Up-Down alternations, dynamics that have been observed during wakefulness, sleep, and anesthesia.

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Bowen W. Zheng, Earl K. Miller, Ila R. Fiete. 2026-06-29. Mean-field theory of rich oscillatory dynamics in low-rank recurrent networks with activity-dependent adaptation. https://arxiv.org/abs/2606.30366

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