6533b854fe1ef96bd12af374
RESEARCH PRODUCT
Ergodicity for a stochastic Hodgkin–Huxley model driven by Ornstein–Uhlenbeck type input
R. HöpfnerEva LöcherbachMichèle Thieullensubject
Statistics and ProbabilityDegenerate diffusion processesWeak Hörmander conditionType (model theory)01 natural sciencesPeriodic ergodicity010104 statistics & probability60H0760J25FOS: Mathematics0101 mathematicsComputingMilieux_MISCELLANEOUSMathematical physicsMathematics60J60Quantitative Biology::Neurons and CognitionProbability (math.PR)010102 general mathematicsErgodicityOrnstein–Uhlenbeck processHodgkin–Huxley model[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]Hodgkin–Huxley model60J60 60J25 60H07Statistics Probability and UncertaintyTime inhomogeneous diffusion processesMathematics - Probabilitydescription
We consider a model describing a neuron and the input it receives from its dendritic tree when this input is a random perturbation of a periodic deterministic signal, driven by an Ornstein-Uhlenbeck process. The neuron itself is modeled by a variant of the classical Hodgkin-Huxley model. Using the existence of an accessible point where the weak Hoermander condition holds and the fact that the coefficients of the system are analytic, we show that the system is non-degenerate. The existence of a Lyapunov function allows to deduce the existence of (at most a finite number of) extremal invariant measures for the process. As a consequence, the complexity of the system is drastically reduced in comparison with the deterministic system.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-11-14 |