RESUMO
In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh-Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is stable. Under specific types of noises, we prove that there exists a global random attractor for the stochastic FHN system. The linearization method is then applied to estimate the firing time and to derive the associated radial equation representing a LIF equation. This result confirms the previous prediction in Ditlevsen and Greenwood (J Math Biol 67(2):239-259, 2013) for the Morris-Lecar neuron model in the bistability regime consisting of a stable fixed point and a stable limit cycle.
Assuntos
Potenciais de Ação/fisiologia , Modelos Neurológicos , Neurônios/fisiologia , Animais , Simulação por Computador , Processos EstocásticosRESUMO
In this paper we prove that under mild conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions. The proofs use estimates in p-variation norms, the construction of greedy sequence of times, and Gronwall-type lemma with the help of Shauder theorem of fixed points.
RESUMO
In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape.
