Xinxin Qie | Search arXiv

arXiv2026

Delay-induced multirhythmicity in a 3-cell inhibitory network

We study the dynamics of a delayed three-cell central pattern generator network using return-map analysis and a phase-reduced description derived from generalized FitzHugh-Nagumo oscillators. The phase model captures the emergence and stability of synchronous, pacemaker, and traveling-wave rhythms and provides a systematic, computationally efficient framework for characterizing the network dynamics beyond direct return-map calculations. We conduct extensive two-parameter analyses of both the full and phase-reduced models, revealing rich multi-rhythmic dynamics and transitions among coexisting rhythmic states. The close agreement between the two descriptions establishes phase reduction as an efficient and reliable framework for characterizing the dynamical organization of delayed neural oscillator networks.

math.DS↗

arXiv2026

Dissecting emerging slow rhythms in delay-coupled neural oscillators

Synaptic transmission delays are ubiquitous in neural circuits and can alter the dynamical repertoire of coupled oscillators quantitatively and qualitatively. Here, we demonstrate that delayed coupling in inhibitory networks introduces an effective slow-fast structure in the phase-difference dynamics, generating low-frequency components that are not due to intrinsic cellular properties, and we show that this behavior is not specific to a particular model structure. The origin of this generic phenomenon is analyzed by numerical continuation and bifurcation analysis, which provides a systematic approach to find such delay-induced slow modulating rhythms. We employ phase reduction based on phase response curves to derive a phase-difference model with delay for mutually inhibitory coupled oscillators, where the individual units are given by the FitzHugh-Nagumo model, the Morris-Lecar model, or a next-generation neural mass model derived from quadratic integrate-and-fire neurons. We use phase planes to study multistability and limit cycles, which correspond to slow modulation of fast oscillations in the full model. Treating the synaptic delay as a bifurcation parameter, we apply numerical continuation to construct delay-dependent bifurcation diagrams. The analysis reveals Hopf, heteroclinic, and saddle-node-of-periodics bifurcations that cause and organize slow rhythmic behavior. Our analysis provides a systematic approach to the search for limit cycles in phase-reduction models corresponding to delay-induced slow rhythms in the original model.

nlin.CD↗