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FitzHugh–Nagumo Model
The FitzHugh–Nagumo model (FHN), named after Richard FitzHugh (1922–2007) who suggested the system in 1961 and J. Nagumo ''et al''. who created the equivalent circuit the following year, describes a prototype of an excitable system (e.g., a neuron). The FHN Model is an example of a relaxation oscillator because, if the external stimulus I_ exceeds a certain threshold value, the system will exhibit a characteristic excursion in phase space, before the variables v and w relax back to their rest values. This behaviour is typical for spike generations (a short, nonlinear elevation of membrane voltage v, diminished over time by a slower, linear recovery variable w) in a neuron after stimulation by an external input current. The equations for this dynamical system read : \dot=v-\frac - w + RI_ : \tau \dot = v+a-b w. The dynamics of this system can be nicely described by zapping between the left and right branch of the cubic nullcline. The FitzHugh–Nagumo model is a sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fitzhugh Nagumo Model Time Domain Graph
Fitzhugh is an England, English Anglo-Normans, Anglo-Norman surname originating in Northamptonshire and Bedfordshire. It is patronymic as the prefix ''Fitz-'' derives from the Latin ''filius'', meaning "son of". Its variants include ''FitzHugh'', ''Fitz-Hugh'', ''Fitz Hugh'', ''fitz Hugh'', and its associated given name turned surname ''Hugh (given name), Hugh''. Fitzhugh is rare as a given name. A family with the surname of Fitzhugh were proven descendants of Acaris, son of Bardolf, a son of Odo, Count of Penthièvre who was a close relative and important ally of William the Conqueror.Early Yorkshire Charters: Volume 5, The Honour of Richmond, Part 2, edited by William Farrer, Charles Travis Clay Surname People with the name Fitzhugh include: *Charles Lane Fitzhugh (1838–1923), an American military officer *Courtney Fitzhugh, American hematologist-oncologist and scientist *Elisabeth West FitzHugh (1926–2017), art conservation scientist *George Fitzhugh (priest) (died 1505), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Van Der Pol Oscillator
In dynamical system, dynamics, the Van der Pol oscillator is a Conservative force, non-conservative oscillator with nonlinearity, non-linear Damping ratio, damping. It evolves in time according to the second-order differential equation: :-\mu(1-x^2)+x= 0, where ''x'' is the position coordinate system, coordinate—which is a function (mathematics), function of the time ''t'', and ''μ'' is a scalar (mathematics), scalar parameter indicating the nonlinearity and the strength of the damping. History The Van der Pol oscillator was originally proposed by the Dutch electrical engineering, electrical engineer and physicist Balthasar van der Pol while he was working at Philips. Van der Pol found stable oscillations, which he subsequently called relaxation oscillator, relaxation-oscillations and are now known as a type of limit cycle in electrical circuits employing vacuum tubes. When these circuits are driven near the limit cycle, they become entrainment (physics), entrained, i.e. the d ... [...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] |
Proc
Proc may refer to: * Proč, a village in eastern Slovakia * '' Proč?'', a 1987 Czech film * procfs or proc filesystem, a special file system (typically mounted to ) in Unix-like operating systems for accessing process information * Protein C (PROC) * Proc, a term in video game terminology * Procedures or process, in the programming language ALGOL 68 * People's Republic of China, the formal name of China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ... * the official acronym for the Canadian House of Commons Standing Committee on Procedure and House Affairs {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theta Model
The theta model, or Ermentrout–Kopell canonical model, is a biological neuron model originally developed to model neurons in the animal Aplysia, and later used in various fields of computational neuroscience. The model is particularly well suited to describe neuron bursting, which are rapid oscillations in the membrane potential of a neuron interrupted by periods of relatively little oscillation. Bursts are often found in neurons responsible for controlling and maintaining steady rhythms. For example, breathing is controlled by a small network of bursting neurons in the brain stem. Of the three main classes of bursting neurons ( square wave bursting, parabolic bursting, and elliptic bursting), the theta model describes parabolic bursting. Parabolic bursting is characterized by a series of bursts that are regulated by a slower external oscillation. This slow oscillation changes the frequency of the faster oscillation so that the frequency curve of the burst pattern resembl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morris–Lecar Model
The Morris–Lecar model is a biological neuron model developed by Catherine Morris and Harold Lecar to reproduce the variety of oscillatory behavior in relation to Ca++ and K+ conductance in the muscle fiber of the giant barnacle . Morris–Lecar neurons exhibit both class I and class II neuron excitability. History Catherine Morris (b. 24 December 1949) is a Canadian biologist. She won a Commonwealth scholarship to study at Cambridge University, where she earned her PhD in 1977. She became a professor at the University of Ottawa in the early 1980s. As of 2015, she is an emeritus professor at the University of Ottawa. Harold Lecar (18 October 1935 – 4 February 2014) was an American professor of biophysics and neurobiology at the University of California Berkeley. He graduated with his PhD in physics from Columbia University in 1963. Experimental method The Morris–Lecar experiments relied on the voltage clamp method established by Keynes ''et al.'' (1973). The principal ... [...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] |
Biological Neuron Model
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] |
Autowave
Autowaves are self-supporting non-linear waves in active media (i.e. those that provide distributed energy sources). The term is generally used in processes where the waves carry relatively low energy, which is necessary for synchronization or switching the active medium. Introduction Relevance and significance In 1980, the Soviet scientists G.R. Ivanitsky, V.I. Krinsky, A.N. Zaikin, A.M. Zhabotinsky, B.P. Belousov became winners of the highest state award of the USSR, Lenin Prize "''for the discovery of a new class of autowave processes and the study of them in disturbance of stability of the distributed excitable systems''." A brief history of autowave researches The first who studied actively the self-oscillations was Academician AA Andronov, and the term "''auto-oscillations''" in Russian terminology was introduced by AA Andronov in 1928. His followers from Lobachevsky University further contributed greatly to the development of ''autowave theory''. The s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balthasar Van Der Pol
Balthasar van der Pol (27 January 1889 – 6 October 1959) was a Dutch physicist. Life and work Van der Pol began his studies of physics in Utrecht in 1911. J. A. Fleming offered van der Pol the use of the Pender Electrical Laboratory at University College for a study of the heuristics of wireless reception on board ships. In England he also worked with J. J. Thomson. Upon his return to the Netherlands, Balthsar worked with Hendrik Lorentz at Teylers Stichting. For his thesis he wrote ''The effect of an ionised gas on electro-magnetic wave propagation and its application to radio, as demonstrated by glow-discharge measurement'' under the supervision of Willem Henri Julius. He was awarded his Ph.D. in 1920. He joined Philips Research Laboratories in 1921, where he worked until his retirement in 1949. As observed by Hendrik Casimir, "Radio might have remained a field of haphazard empiricism along with wild commercial ventures, but for the influence of men like Van der Pol wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fitzhugh Nagumo Phase Space Graph
Fitzhugh is an English Anglo-Norman surname originating in Northamptonshire and Bedfordshire. It is patronymic as the prefix ''Fitz-'' derives from the Latin ''filius'', meaning "son of". Its variants include ''FitzHugh'', ''Fitz-Hugh'', ''Fitz Hugh'', ''fitz Hugh'', and its associated given name turned surname ''Hugh''. Fitzhugh is rare as a given name. A family with the surname of Fitzhugh were proven descendants of Acaris, son of Bardolf, a son of Odo, Count of Penthièvre who was a close relative and important ally of William the Conqueror.Early Yorkshire Charters: Volume 5, The Honour of Richmond, Part 2, edited by William Farrer, Charles Travis Clay Surname People with the name Fitzhugh include: *Charles Lane Fitzhugh (1838–1923), an American military officer *Courtney Fitzhugh, American hematologist-oncologist and scientist *Elisabeth West FitzHugh (1926–2017), art conservation scientist *George Fitzhugh (priest) (died 1505), chancellor of Cambridge University and Dean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
