Exp-function method for solving Huxley equation.
Global existence of periodic solutions in a simplified four-neuron BAM neural network model with multiple delays.
Global exponential stability of pseudo almost automorphic solutions for delayed Cohen-Grosberg neural networks with measure
We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a -pseudo almost automorphic solution. The...
How and why do neurons generate complex rhythms with various frequencies?
Identifying generalized Fitzhugh-Nagumo equation from a numerical solution of Hodgkin-Huxley model.
Indecision in Neural Decision Making Models
Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition....
Information processing in the retina: computer model and some conclusions
K otázke fyzikálneho významu Hodgkin-Huxleyho empirických rovníc pre iónové vodivosti počas vzruchu
Model neuronu
Model neuronu s možností samoorganizace
Model-based analysis and optimization of the mapping of cortical sources in the spontaneous scalp EEG.
Multiple neural network integration using a binary decision tree to improve the ECG signal recognition accuracy
The paper presents a new system for ECG (ElectroCardioGraphy) signal recognition using different neural classifiers and a binary decision tree to provide one more processing stage to give the final recognition result. As the base classifiers, the three classical neural models, i.e., the MLP (Multi Layer Perceptron), modified TSK (Takagi-Sugeno-Kang) and the SVM (Support Vector Machine), will be applied. The coefficients in ECG signal decomposition using Hermite basis functions and the peak-to-peak...
Neurons: a numerical approach.
Nonlinear filtering of oscillatory measurements in cardiovascular applications.
Numerical simulations of effects of multiple neurotransmission on intestinal propulsion of a non-deformable bolus.
Numerical study of the stopping of aura during migraine
This work is devoted to the study of migraine with aura in the human brain. Following [6], we class migraine as a propagation of a wave of depolarization through the cells. The mathematical model used, based on a reaction-diffusion equation, is briefly presented. The equation is considered in a duct containing a bend, in order to model one of the numerous circumvolutions of the brain. For a wide set of parameters, one can establish the existence...
On Chaotic Subthreshold Oscillations in a Simple Neuronal Model
In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.
Oscillation and global asymptotic stability of a neuronic equation with two delays.
Past, Present and Future of Brain Stimulation
Recent technological advances including brain imaging (higher resolution in space and time), miniaturization of integrated circuits (nanotechnologies), and acceleration of computation speed (Moore’s Law), combined with interpenetration between neuroscience, mathematics, and physics have led to the development of more biologically plausible computational models and novel therapeutic strategies. Today, mathematical models of irreversible medical conditions...
Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops
We study the coexistence of multiple periodic solutions for an analogue of the integrate-and-fire neuron model of two-neuron recurrent inhibitory loops with delayed feedback, which incorporates the firing process and absolute refractory period. Upon receiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits a spike with a pattern-related delay, in addition to the synaptic delay. We present a theoretical framework to view...