Subthreshold oscillations can be found in different neural systems. Some mathematical models of bursting
neurons also manifest slow oscillations that are more or less independent from fast spiking process and becomes
subthreshold when spiking subsystem is set in excitable regime. Because neural activity is known to be heavily
influenced by a variety of noisy processes, it is important to understand how the subthreshold oscillations can
change the response of neural system on noisy stimulus.
It is typically assumed that generation of spike does not affect slow subsystem. However, such one-way
connection between slow and fast subsystems is not the case for many neural models where fast and slow ionic
currents share the same equation for transmembrane potential (for example, well known Huber-Braun model).
Definitely, the generation of fast action potential can affect the slow ionic currents. Thus, being excited by
noise, such neural system could show different firing patterns depending on how slow subsystem is affected by
the fast one. To address this problem we propose the generalized model consisting of two FitzHugh-Nagumo
systems that are set in different operating regimes and thus play the role of fast excitable and slow self-sustained
subsystems. With this model, we study how the noise-induced firing patterns depend on different variants of
fast-to-slow coupling between subsystems. The corresponding changes in ISI distribution as well as underlying
nonlinear mechanisms are discussed.
We study the effect of noise on a generalized mathematical model for small neural-glial ensemble. In deterministic regime, our model predicts long-term potentiation of the postsynaptic neuron as well as various calcium transients in response to the activation of glion via different pathways. Being activated by noise, the presynaptic neuron shows the irregular firing pattern. We consider how the glion (a generic glial cell) moderates the regime of the postsynaptic neuron. We observe the number of noise induced effects, such as different types of post-excitatory behavior of the postsynaptic neuron at small noise intensity and the long-term potentiation of the postsynaptic neuron at some optimal noise intensity.
In order to treat the effect of subthreshold dynamics on noisy neuron behavior we focus on parameters region of FitzHugh-Nagumo
model close to the so called canard-explosion. Such parameter region corresponds to transition from excitable regime to continuous spiking. We observe the number of noise-induced effects, such as (i) noise-induced stabilization of firing frequency; (ii) noise-induced
suppression of spiking; (iii) noise-induced chaos. We show that for small ensemble of resonator-type neurons activated by noise there is the global maxima of firing frequency at some optimal noise intensity. The underlying mechanisms of such behavior are closely related to noise-activated subthreshold dynamics.