{"ID":5346738,"CreatedAt":"2026-06-30T04:09:55.830587294Z","UpdatedAt":"2026-07-02T14:28:49.359749133Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.30366","arxiv_id":"2606.30366","title":"Mean-field theory of rich oscillatory dynamics in low-rank recurrent networks with activity-dependent adaptation","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.","short_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...","url_abs":"https://arxiv.org/abs/2606.30366","url_pdf":"https://arxiv.org/pdf/2606.30366v1","authors":"[\"Bowen W. Zheng\",\"Earl K. Miller\",\"Ila R. Fiete\"]","published":"2026-06-29T14:32:19Z","proceeding":"q-bio.NC","tasks":"[\"q-bio.NC\"]","methods":"[]","has_code":false}