ArXiv paper reveals slow rhythms from synaptic delays in neural oscillators

In a new preprint on arXiv (2606.20733), researchers Xinxin Qie, Matteo Martin, Shenquan Liu, and Morten Gram Pedersen demonstrate that synaptic transmission delays in coupled inhibitory neural oscillators can produce slow rhythmic activity that does not originate from intrinsic cellular properties. Using numerical continuation and bifurcation analysis, they reveal how delayed coupling introduces an effective slow-fast structure in phase-difference dynamics, leading to low-frequency components. The team employed phase reduction based on phase response curves for three distinct models—FitzHugh-Nagumo, Morris-Lecar, and a next-generation neural mass model derived from quadratic integrate-and-fire neurons—to confirm the phenomenon is model-independent.

By treating synaptic delay as a bifurcation parameter, the analysis identifies Hopf, heteroclinic, and saddle-node-of-periodics bifurcations that organize the slow rhythmic behavior. Phase-plane analysis of the reduced phase-difference model reveals multistability and limit cycles corresponding to slow modulation of fast oscillations in the full system. This systematic approach offers a mathematical framework for predicting and analyzing delay-induced slow rhythms, with implications for understanding brain oscillations, neural synchrony, and pathological rhythms such as tremors or epileptic activity. The work bridges nonlinear dynamics, computational neuroscience, and quantitative biology.