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How is reliable physiological function maintained in cells despite considerable variability in the values of key parameters of multiple interacting processes that govern that function? Here we use the classic Hodgkin-Huxley formulation of…
This paper presents an overview of some techniques and concepts coming from dynamical system theory and used for the analysis of dynamical neural networks models. In a first section, we describe the dynamics of the neuron, starting from the…
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…
This article is devoted to the theoretical and numerical analysis of a network of excitatory and inhibitory neurons of Hodgkin-Huxley (HH) type, for which the topology is inspired by that of a single local layer of visual cortex V1. Our…
The generation of action potential brings into play specific mechanosensory stimuli manifest in the variation of membrane capacitance, resulting from the selective membrane permeability to ions exchanges and testifying to the central role…
In this study we derive the governing equations for mesoscopic collective activity in the cortex, starting from the generic Hodgkin-Huxley equations for microscopic cell dynamics. For simplicity, and to maintain focus on the essential…
Fifty years ago, Fitzugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold…
Multi-compartment Hodgkin-Huxley models are biophysical models of how electrical signals propagate throughout a neuron, and they form the basis of our knowledge of neural computation at the cellular level. However, these models have many…
The analyses presented herein demonstrate that neuronal electrical activity can be consistently interpreted as a manifestation of murburn redox-mediated electronic dynamics rather than as a process fundamentally driven by transmembrane…
Physics perfectly describes neuronal operation, provided that we take into account that biology uses slow, positively charged ions rather than electrons as charge carriers and remove untested ad hoc hypotheses that contradict science's…
A spiking neuron ``computes'' by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a…
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…
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…
Recent experimental and theoretical studies show that energy efficiency, which measures the amount of information processed by a neuron with per unit of energy consumption, plays an important role in the evolution of neural systems. Here,…
Neuronal excitability is the phenomena that describes action potential generation due to a stimulus input. Commonly, neuronal excitability is divided into two classes: Type I and Type II, both having different properties that affect…
Trans-membrane gradients and fluxes of cations (H+, Na+, K+, etc.) were deemed to be the rationale of electrical activities of aerobic cells/organelles, as per classical perceptions. Murburn concept (an umbrella of theorization based in…
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,…
By means of the concepts of factorial moment, return map and NM estimator, we analyze some responses of a HH neuron to various types of spike-train inputs. The corresponding fractal dimensions and values of NM estimators can describe the…
In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of…
This paper deals with the mathematical modelling of signal propagation in nerve fibres. Due to the complexity of the processes where electrical, mechanical, and thermal effects are coupled, a phenomenological approach helps to build…