Related papers: A Mathematical Characterization of Neural Activati…
Neurons are the central biological objects in understanding how the brain works. The famous Hodgkin-Huxley model, which describes how action potentials of a neuron are initiated and propagated, consists of four coupled nonlinear…
The influence of time delay in systems of two coupled excitable neurons is studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in the coupling between neurons or in a self-feedback loop. The stochastic…
We study the phenomenological model of ensemble of two FitzHugh-Nagumo neuron-like elements with symmetric excitatory couplings. The main advantage of proposed model is the new approach to model of coupling which is implemented by smooth…
Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been…
An electronic circuit device, inspired on the FitzHugh-Nagumo model of neuronal excitability, was constructed and shown to operate with characteristics compatible with those of biological sensory neurons. The nonlinear dynamical model of…
Despite intensive research, the mechanisms underlying how neurons encode external inputs remain poorly understood. Recent work has focused on the response of a single neuron to a weak, subthreshold periodic signal. By simulating the…
Excitable membranes are an important type of nonlinear dynamical system and their study can be used to provide a connection between physical and biological circuits. We discuss two models of excitable membranes important in cardiac and…
Modern mobile applications heavily rely on the notification system to acquire daily active users and enhance user engagement. Being able to proactively reach users, the system has to decide when to send notifications to users. Although many…
The slow dynamics of nearly stationary patterns in a FitzHugh-Nagumo model are studied using a phase dynamics approach. A Cross-Newell phase equation describing slow and weak modulations of periodic stationary solutions is derived. The…
Spiking Neural Networks (SNNs) are a promising framework for event-driven temporal processing. Prior work has improved temporal modeling through richer neuron dynamics and network-level mechanisms such as recurrence and delays, but it…
Dynamics of class II neurons, firing frequencies of which are strongly regulated by the inherent neuronal property, have been extensively studied since the formulation of the Hodgkin--Huxley model in 1952. However, how class II neurons…
Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates…
This paper predicts the ability to externally control the firing times of a cortical neuron whose behavior follows the Izhikevich neuron model. The Izhikevich neuron model provides an efficient and biologically plausible method to track a…
We discuss the synchronization of coupled neurons which are modelled as FitzHugh-Nagumo systems. As smallest entity in a larger network, we focus on two diffusively coupled subsystems, which can be interpreted as two mutually interacting…
Neurons encode and transmit information in spike sequences. However, despite the effort devoted to quantify their information content, little progress has been made in this regard. Here we use a nonlinear method of time-series analysis…
The excitability property of spiking neurons describes their capability to output an action potential as a real-time response to an input synaptic excitation current and is central to the event-based neuromorphic computing paradigm. The…
Deep Brain Stimulation (DBS) is effective in treating neurological disorders but involves invasive surgery. Non-invasive DBS aims to overcome surgical risks by means of externally applied electromagnetic fields. In this work, we present a…
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or…
We propose a nonlinear one-dimensional FitzHugh--Nagumo neuronal model with an asymmetric potential driven by both a high-frequency and a low-frequency signal. Our numerical analysis focuses on the influence of a state-dependent time delay…
Closed-loop neural stimulation provides novel therapies for neurological diseases such as Parkinson's disease (PD), but it is not yet clear whether artificial intelligence (AI) techniques can tailor closed-loop stimulation to individual…