14 papers · ranked by Valyu relevance
Soheil Saghafi, Pejman Sanaei
Resonance and synchronized rhythm are important phenomena and can be either constructive or destructive in dynamical systems in the nature, specifically in biology. There are many examples showing that the human’s body organs must maintain their rhythm in order to function properly. For instance, in the brain…
Jürgen Geiser, Dennis Ogiermann
We are motivated to approximate solutions of a Hodgkin-Huxley type model with implicit methods. As a representative we chose a psychiatric disease model containing stable as well as chaotic cycling behaviour. We analyze the bifurcation pattern and show that some implicit methods help to preserve the limit cycles of…
Yue Zhang, Kuanquan Wang, Yongfeng Yuan, Dong Sui + 1 more
Hodgkin-Huxley (HH) equation is the first cell computing model in the world and pioneered the use of model to study electrophysiological problems. The model consists of four differential equations which are based on the experimental data of ion channels. Maximal conductance is an important characteristic of different…
Ulises Chialva, Vicente González Boscá, Horacio G. Rotstein
The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents.…
Wondimu Teka, David Stockton, Fidel Santamaria, Kim T. Blackwell
We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional…
Michel Peyrard
In the last fifteen years a debate emerged about the validity of the famous Hodgkin-Huxley model for nerve impulse. Mechanical models have been proposed. This note reviews the experimental properties of the nerve impulse and discusses the proposed alternatives. The experimental data, which rule out some of the…
Hillel Ori, Hananel Hazan, Eve Marder, Shimon Marom
Excitability – a threshold governed transient in transmembrane voltage – is a fundamental physiological process that controls the function of the heart, endocrine, muscles and neuronal tissues. The 1950’s Hodgkin and Huxley explicit formulation provides a mathematical framework for understanding excitability, as the…
Alon Korngreen
Biophysically detailed neuron models are often built as a one-way pipeline in which voltage-clamp data are reduced to a single set of best-fit channel parameters, which are then combined into a deterministic spiking model. This practice discards experimentally observed variability and obscures the mechanisms by which…
Oguzhan Derebasi, Murat Işık, Oguzhan Demirag, Dilek Göksel Duru + 1 more
'Anup Das'] Guillain-Barre syndrome is a rare neurological condition in which the human immune system attacks the peripheral nervous system. A peripheral nervous system appears as a diffusively connected system of mathematical models of neuron models, and the system's period becomes shorter than the periods of each…
Ruben Schoeters, Thomas Tarnaud, Luc Martens, Wout Joseph + 2 more
Optogenetics has a lot of potential to become an effective neuromodulative therapy for clinical application. Selecting the correct opsin is crucial to have an optimal optogenetic tool. With computational modeling, the neuronal response to the current dynamics of an opsin can be extensively and systematically tested.…
Zhengdao Chen, Baranidharan Raman, Ari Stern
Motivated by the Hodgkin–Huxley model of neuronal dynamics, we study explicit numerical integrators for "conditionally linear" systems of ordinary differential equations. We show that splitting and composition methods, when applied to the Van der Pol oscillator and to the Hodgkin–Huxley model, do a better job of…
weiwei zhang
The Adaptive Exponential Integrate-and-Fire (AdEx) model is a simplified framework that effectively characterizes neuronal electrical activity. The aim of this paper is to employ phase plane analysis to systematically investigate diverse firing patterns generated by the AdEx model under varying parametric conditions.…
Juris Viksna, Karlis Cerans, Lelde Lace, Gatis Melkus
We introduce the formal notion of representation graphs, encapsulating the state space structure of gene regulatory network models in a compact and concise form that highlights the most significant features of stable states and differentiation processes leading to distinct stability regions. The concept has been…
Gesina Menz, Stefan Engblom
Multi-Framework Approach Authors: ['Gesina Menz' 'Stefan Engblom'] In this work we model the dynamics for the transcription factor Hairy and enhancer of split-1 (Hes1), whose expression oscillates during neural development, and which critically enables stable fate decision in the embryonic brain. We design…