2025/11/20 by Robin Wroblowski, Rodolphe Sepulchre, Wroblowski, Robin +1
Computer Science · Neuroscience · Physics and Astronomy · #Chaos control and synchronization #Control theory (sociology) #Describing function #Function (biology) #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Operator (biology) #Phase (matter) #Phase response #Phase response curve #Train #Transfer function
paper · pdf · doi:10.48550/arxiv.2511.16235
openalex publication_date 2025/11/20 · openalex created_date 2025/11/23 · openalex updated_date 2026/08/05
The describing function (DF) and phase response curve (PRC) are classical tools for the analysis of feedback oscillations and rhythmic behaviors, widely used across control engineering, biology, and neuroscience. These tools are known to have limitations in networks of relaxation oscillators and excitable systems. For this reason, the paper proposes a novel approach tailored to excitable systems. Our analysis focuses on the discrete-event operator mapping input trains of events to output trains of events. The methodology is illustrated on the excitability model of Hodgkin-Huxley. The proposed framework provides a basis for designing and analyzing central pattern generators in networks of excitable neurons, with direct relevance to neuromorphic control and neurophysiology.