Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations
DOI10.1007/s10884-022-10148-zarXiv2107.02468OpenAlexW3178706396WikidataQ115382873 ScholiaQ115382873MaRDI QIDQ6196000
Publication date: 14 March 2024
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2107.02468
nonlinear Fokker-Planck equationperiodic behaviornormally hyperbolic manifoldsmean-field systemsMcKean-Vlasov processisochron map
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Dynamical systems in biology (37N25) Neural networks for/in biological studies, artificial life and related topics (92B20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Population dynamics (general) (92D25) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Vlasov equations (35Q83) Fokker-Planck equations (35Q84) PDEs on manifolds (35R01)
Cites Work
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- On a kinetic FitzHugh-Nagumo model of neuronal network
- Clarification and complement to ``Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons
- Convergence to the equilibria for self-stabilizing processes in double-well landscape
- Synchronization and random long time dynamics for mean-field plane rotators
- Collective periodicity in mean-field models of cooperative behavior
- Approximately invariant manifolds and global dynamics of spike states
- Semigroups of linear operators and applications to partial differential equations
- Periodic behavior of the stochastic Brusselator in the mean-field limit
- Geometric theory of semilinear parabolic equations
- Geometric singular perturbation theory for ordinary differential equations
- Isochrons and phaseless sets
- Nonlinear self-stabilizing processes. II: Convergence to invariant probability
- Oscillatory behavior in a model of non-Markovian mean field interacting spins
- Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo model
- Hopf bifurcation in a mean-field model of spiking neurons
- Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons
- Emergence of oscillatory behaviors for excitable systems with noise and mean-field interaction: a slow-fast dynamics approach
- Noise, interaction, nonlinear dynamics and the origin of rhythmic behaviors
- Multi-class oscillating systems of interacting neurons
- Probabilistic approach for granular media equations in the non-uniformly convex case
- Existence and persistence of invariant manifolds for semiflows in Banach space
- Transitions in Active Rotator Systems: Invariant Hyperbolic Manifold Approach
- Analysis and Geometry of Markov Diffusion Operators
- Clamping and Synchronization in the Strongly Coupled FitzHugh--Nagumo Model
- A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
- Rhythmic behavior of an Ising Model with dissipation at low temperature
- Special Functions and Orthogonal Polynomials
- Invariant manifolds
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