Related papers: A Mathematical Characterization of Neural Activati…
For decades, focal non-invasive neuromodulation of deep brain regions has not been possible because of the steep depth-focality trade-off of conventional non-invasive brain stimulation (NIBS) techniques, such as transcranial magnetic…
The use of high-frequency currents in neurostimulation has received increased attention in recent years due to its varied effects on tissues and cells. Nonlinear differential equations are commonly used as models for Neurons, and averaging…
We investigate feedback control of the cooperative dynamics of two coupled neural oscillators that is induced merely by external noise. The interacting neurons are modelled as FitzHugh-Nagumo systems with parameter values at which no…
We investigate neuronal excitability in the Hodgkin-Huxley model under temporal interference (TI) stimulation in a previously unexplored sub-Hz resonant regime and uncover a striking nonlinear response that we term 'multi-tongue frequency…
Being an example for a relaxation oscillator, the FitzHugh-Nagumo model has been widely employed for describing the generation of action potentials. In this paper, we begin with a biological interpretation of what the subsequent…
Spinal cord injury (SCI) is a debilitating condition that often results in significant motor and sensory deficits, impacting the quality of life. Current rehabilitation methods, including physical therapy and electrical stimulation, offer…
Understanding how external stimuli propagate in neural systems is an important challenge in the fields of neuroscience and nonlinear dynamics. Despite extensive studies over several decades, this problem remains poorly understood. In this…
Periodic pulse train stimulation is generically used to study the function of the nervous system and to counteract disease-related neuronal activity, e.g., collective periodic neuronal oscillations. The efficient control of neuronal…
Brain operates at remarkably low signal power. It has been noted that noise may play a constructive role in neural networks and facilitate the subthreshold signaling. The process of spiking pattern excitation at the characteristic neuronal…
A new type of non-invasive deep-brain stimulation is conceived and demonstrated by computer simulations. The process is based on spatio-temporal Fourier synthesis using multiple electrode pairs with sinusoidal current drive to limit skin…
This paper studies the phenomenon of conduction block in model neurons using high-frequency biphasic stimulation (HFBS). The focus is investigating the triggering of undesired onset action potentials when the HFBS is turned on. The approach…
We examine the response of type II excitable neurons to trains of synaptic pulses, as a function of the pulse frequency and amplitude. We show that the resonant behavior characteristic of type II excitability, already described for harmonic…
Background and Objective: Transcranial temporal interference stimulation (tTIS) is a promising non-invasive brain stimulation technique in which interference between electrical current fields extends the possibilities of electrical brain…
We propose theoretical methods to infer coupling strength and noise intensity simultaneously through an observation of spike timing in two well-synchronized noisy oscillators. A phase oscillator model is applied to derive formulae relating…
In various neurological disorders spatio-temporal excitation patterns constitute examples of excitable behavior emerging from pathological pathways. During migraine, seizure, and stroke an initially localized pathological state can…
The FitzHugh-Nagumo equation, originally conceived in neuroscience during the 1960s, became a key model providing a simplified view of excitable neuron cell behavior. Its applicability, however, extends beyond neuroscience into fields like…
We investigate a possibility of realization of structurally stable chaotic dynamics in neural systems. The considered model of interacting neurons consists of a pair of coupled FitzHugh-Nagumo systems, with the parameters being periodically…
The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast…
Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed…
We consider the long-time behavior of a population of mean-field oscillators modeling the activity of interacting excitable neurons in large population. Each neuron is represented by its voltage and recovery variables, which are solution to…