Related papers: Multimodal transition and stochastic antiresonance…
In this paper, we analyze the effect of the redistribution of the transmembrane ion channels in the axon caused by longitudinal acoustic vibrations of the membrane. These oscillations can be excited by an external source of ultrasound and…
Recently [1], we proposed a new way to engineer a flexible acoustomechanical coupling between the center-of-mass motion of an isolated micromagnet and one of its internal acoustic phonons by using a magnon as a passive mediator. In our…
Numerical investigations have been made of responses of a Hodgkin-Huxley (HH) neuron to spike-train inputs whose interspike interval (ISI) is modulated by deterministic, semi-deterministic (chaotic) and stochastic signals. As deterministic…
Numerical calculations have been made on the spike-train response of a pair of Hodgkin-Huxley (HH) neurons coupled by synapses and axons with time delay. The recurrent excitatory-excitatory, inhibitory-inhibitory, excitatory-inhibitory, and…
Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often, these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the…
We present a novel and global three-dimensional reduction of a non-dimensionalised version of the four-dimensional Hodgkin-Huxley equations [J. Rubin and M. Wechselberger, Giant squid--hidden canard: the 3D geometry of the Hodgkin-Huxley…
We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients when the drift depends on time and space and is periodic in the time argument. There is no time…
This paper presents a rigorous mathematical analysis, alongside simulation studies, of a spatially extended stochastic electrophysiology model, the Hodgkin-Huxley model of the squid giant axon being a classical example. Although most…
The generation and conduction of action potentials represents a fundamental means of communication in the nervous system, and is a metabolically expensive process. In this paper, we investigate the energy efficiency of neural systems in a…
Micron-sized superconducting interference devices ($\mu$-SQUIDs) based on constrictions optimized for minimizing thermal runaway are shown to exhibit voltage oscillations with applied magnetic flux despite their hysteretic behavior. We…
Neuronal models based on the Hodgkin-Huxley equation form a fundamental framework in the field of computational neuroscience. While the neuronal state is often modeled deterministically, experimental recordings show stochastic fluctuations,…
Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane but also contribute to an additional charging of the cell membrane resulting in the…
The stochastic Hodgkin-Huxley neurons considered in this paper replace time-constant deterministic input $a dt$ of the classical deterministic model by increments $\vartheta dt + dX_t$ of a stochastic process: $X$ is Ornstein-Uhlenbeck with…
Classical models for predicting current flow in excitable cells such as axons, originally proposed by Hodgkin and Huxley, rely on empirical voltage-gating parameters that quantify ion transport across sodium and potassium ion channels. We…
Using a stochastic generalization of the Hodgkin–Huxley model, we consider the influence of intrinsic channel noise on the synchronization between the spiking activity of the excitable membrane and an externally applied periodic…
Noise can shape the firing behaviors of neurons. Here, we show that noise acting on the fast variable of the Hedgehog burster can tune the spike counts of bursts via the self-induced stochastic resonance (SISR) phenomenon. Using the…
We present a phenomenological reduced-order model to capture the transition to thermoacoustic instability in turbulent combustors. The model is based on the framework of synchronization and considers the acoustic field and the unsteady heat…
Low-frequency molecular fluctuations in the translational nonequilibrium zone of one-dimensional strong shock waves are characterised for the first time in a kinetic collisional framework in the Mach number range $2\le M\le 10$. Our…
We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling…
This work proposes a two-dimensional electrophysiological model for describing neuronal responses to external electric stimuli under patch-clamped conditions. Our proposed model successfully captures the key features of the Hodgkin-Huxley…