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Hindmarsh–Rose Model
The Hindmarsh–Rose model of neuronal activity is aimed to study the spiking-bursting behavior of the membrane potential observed in experiments made with a single neuron. The relevant variable is the membrane potential, ''x''(''t''), which is written in dimensionless units. There are two more variables, ''y''(''t'') and ''z''(''t''), which take into account the transport of ions across the membrane through the ion channels. The transport of sodium and potassium ions is made through fast ion channels and its rate is measured by ''y''(''t''), which is called the spiking variable. ''z''(''t'') corresponds to an adaptation current, which is incremented at every spike, leading to a decrease in the firing rate. Then, the Hindmarsh–Rose model has the mathematical form of a system of three nonlinear ordinary differential equations on the dimensionless dynamical variables ''x''(''t''), ''y''(''t''), and ''z''(''t''). They read: : \begin \frac &= y+\phi(x)-z+I, \\ \frac &= \psi(x)-y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neuron
A neuron, neurone, or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous tissue in all animals except sponges and placozoa. Non-animals like plants and fungi do not have nerve cells. Neurons are typically classified into three types based on their function. Sensory neurons respond to stimuli such as touch, sound, or light that affect the cells of the sensory organs, and they send signals to the spinal cord or brain. Motor neurons receive signals from the brain and spinal cord to control everything from muscle contractions to glandular output. Interneurons connect neurons to other neurons within the same region of the brain or spinal cord. When multiple neurons are connected together, they form what is called a neural circuit. A typical neuron consists of a cell body (soma), dendrites, and a single axon. The soma is a compact structure, and the axon and dend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biological Neuron Models
Biological neuron models, also known as a spiking neuron models, are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecond in duration, called action potentials or spikes (Fig. 2). Since spikes are transmitted along the axon and synapses from the sending neuron to many other neurons, spiking neurons are considered to be a major information processing unit of the nervous system. Spiking neuron models can be divided into different categories: the most detailed mathematical models are biophysical neuron models (also called Hodgkin-Huxley models) that describe the membrane voltage as a function of the input current and the activation of ion channels. Mathematically simpler are integrate-and-fire models that describe the membrane voltage as a function of the input current and predict the spike times without a description of the biophysical processes that shape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrophysiology
Electrophysiology (from Greek , ''ēlektron'', "amber" etymology of "electron"">Electron#Etymology">etymology of "electron" , ''physis'', "nature, origin"; and , '' -logia'') is the branch of physiology that studies the electrical properties of biological cells and tissues. It involves measurements of voltage changes or electric current or manipulations on a wide variety of scales from single ion channel proteins to whole organs like the heart. In neuroscience, it includes measurements of the electrical activity of neurons, and, in particular, action potential activity. Recordings of large-scale electric signals from the nervous system, such as electroencephalography, may also be referred to as electrophysiological recordings. They are useful for electrodiagnosis and monitoring. Definition and scope Classical electrophysiological techniques Principle and mechanisms Electrophysiology is the branch of physiology that pertains broadly to the flow of ions (ion current) in biologi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Systems
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chialvo Map
The Chialvo map is a two-dimensional map proposed by Dante R. Chialvo in 1995 to describe the generic dynamics of excitable systems. The model is inspired by Kunihiko Kaneko's Coupled map lattice (CML) numerical approach which considers time and space as discrete variables but state as a continuous one. Later on Rulkov popularized a similar approach. By using only three parameters the model is able to efficiently mimic generic neuronal dynamics in computational simulations, as single elements or as parts of inter-connected networks. The model The model is an iterative map where at each time step, the behavior of one neuron is updated as the following equations: \begin x_ = & f(x_n,y_n) = x_n^2 \exp+k \\ y_ =& g(x_n,y_n) = ay_n-bx_n+c \\ \end in which, x is called activation or action potential variable, and y is the recovery variable. The model has four parameters, k is a time-dependent additive perturbation or a constant bias, a is the time constant of recovery (a<1) [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rulkov Map
The Rulkov map is a two-dimensional iterated map used to model a biological neuron. It was proposed by Nikolai F. Rulkov in 2001."Modelling of spiking-bursting neural behavior using two dimensional map/ref> The use of this map to study neural networks has computational advantages because the map is easier to iterate than a continuous dynamical system. This saves memory and simplifies the computation of large neural networks. The model The Rulkov map, with n as discrete time, can be represented by the following dynamical equations: :x_=\frac+y_n :y_=y_n-\mu(x_-\sigma) where x represents the membrane potential of the neuron. The variable y in the model is a slow variable due to a very small value of \mu (0 < \mu << 1). Unlike variable , variable does not have explicit biological meaning, though some analogy to gating variables can be drawn. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Oscillation
Neural oscillations, or brainwaves, are rhythmic or repetitive patterns of neural activity in the central nervous system. Neural tissue can generate oscillatory activity in many ways, driven either by mechanisms within individual neurons or by interactions between neurons. In individual neurons, oscillations can appear either as oscillations in membrane potential or as rhythmic patterns of action potentials, which then produce oscillatory activation of post-synaptic neurons. At the level of neural ensembles, synchronized activity of large numbers of neurons can give rise to macroscopic oscillations, which can be observed in an electroencephalogram. Oscillatory activity in groups of neurons generally arises from feedback connections between the neurons that result in the synchronization of their firing patterns. The interaction between neurons can give rise to oscillations at a different frequency than the firing frequency of individual neurons. A well-known example of macrosco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Neuroscience
Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system. Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous. The term mathematical neuroscience is also used sometimes, to stress the quantitative nature of the field. Computational neuroscience focuses on the description of biologically plausible neurons (and neural systems) and their physiology and dynamics, and it is therefore not directly concerned with biologically unrealistic models used in connectionism, control theory, cybernetics, quantitative psychology, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hodgkin–Huxley Model
The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical characteristics of excitable cells such as neurons and muscle cells. It is a continuous-time dynamical system. Alan Hodgkin and Andrew Huxley described the model in 1952 to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon. They received the 1963 Nobel Prize in Physiology or Medicine for this work. Basic components The typical Hodgkin–Huxley model treats each component of an excitable cell as an electrical element (as shown in the figure). The lipid bilayer is represented as a capacitance (Cm). Voltage-gated ion channels are represented by electrical conductances (''g''''n'', where ''n'' is the specific ion channel) that depend on both voltage and time. Leak channels are rep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ephaptic Coupling
Ephaptic coupling is a form of communication within the nervous system and is distinct from direct communication systems like electrical synapses and chemical synapses. It may refer to the coupling of adjacent (touching) nerve fibers caused by the exchange of ions between the cells, or it may refer to coupling of nerve fibers as a result of local electric fields.Aur D., Jog, MS. (2010) ''Neuroelectrodynamics: Understanding the brain language'', IOS Press, In either case ephaptic coupling can influence the synchronization and timing of action potential firing in neurons. Myelination is thought to inhibit ephaptic interactions. History and etymology The idea that the electrical activity generated by nervous tissue may influence the activity of surrounding nervous tissue is one that dates back to the late 19th century. Early experiments, like those by du Bois-Reymond, demonstrated that the firing of a primary nerve may induce the firing of an adjacent secondary nerve (termed "seco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. The butterfly effect, an underlying principle of chaos, describes how a small change in one state of a deterministic nonlinear system can result in large differences in a later state (meaning that there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause a tornado in Texas. Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Action Potential
An action potential occurs when the membrane potential of a specific cell location rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and in some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells. In neurons, action potentials play a central role in cell-cell communication by providing for—or with regard to saltatory conduction, assisting—the propagation of signals along the neuron's axon toward synaptic boutons situated at the ends of an axon; these signals can then connect with other neurons at synapses, or to motor cells or glands. In other types of cells, their main function is to activate intracellular processes. In muscle cells, for example, an action potential is the first step in the chain of events l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
