Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo model

DOI10.1214/20-AAP1598zbMath1479.60198arXiv1811.00305OpenAlexW3146680659MaRDI QIDQ2240825

Christophe Poquet, Eric Luçon

Publication date: 4 November 2021

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.00305

zbMATH Keywords

excitable systemsWasserstein distanceFitzHugh-Nagumo modelnonlinear Fokker-Planck equationslow-fast dynamicsmean-field systemsMcKean-Vlasov processnoise-induced dynamics

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Neural biology (92C20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Dynamic and nonequilibrium phase transitions (general) in statistical mechanics (82C26) Fokker-Planck equations (35Q84)

Related Items

Interacting Hawkes processes with multiplicative inhibition, Noise-induced periodicity in a frustrated network of interacting diffusions, Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations, Hopf bifurcation in a mean-field model of spiking neurons, Clamping and Synchronization in the Strongly Coupled FitzHugh--Nagumo Model, Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction: a slow-fast dynamics approach, Effects of local fields in a dissipative Curie-Weiss model: Bautin bifurcation and large self-sustained oscillations

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