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Periodicity induced by noise and interaction in the kinetic mean-field FitzHugh-Nagumo model
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We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented by its voltage and recovery variables, which are solution to a FitzHugh-Nagumo system, and interacts with the rest of the population through a mean-field linear coupling, in the presence of noise. The aim of the paper is to study the emergence of collective oscillatory behaviors induced by noise and interaction on such a system. The main difficulty of the present analysis is that we consider the kinetic case, where interaction and noise are only imposed on the voltage variable. We prove the existence of a stable cycle for the infinite population system, in a regime where the local dynamics is small.
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Statistical estimation of a mean-field FitzHugh-Nagumo model
The paper proves a Bernstein inequality and an oracle inequality for kernel estimation of the Vlasov-Fokker-Planck density, and gives a moment estimator for FitzHugh-Nagumo parameters that contains algebraic errors in...
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