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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] |
Dynamics Of The Van Der Pol Oscillator
Dynamics (from Greek δυναμικός ''dynamikos'' "powerful", from δύναμις ''dynamis'' "power") or dynamic may refer to: Physics and engineering * Dynamics (mechanics) ** Aerodynamics, the study of the motion of air ** Analytical dynamics, the motion of bodies as induced by external forces ** Brownian dynamics, the occurrence of Langevin dynamics in the motion of particles in solution ** File dynamics, stochastic motion of particles in a channel ** Flight dynamics, the science of aircraft and spacecraft design ** Fluid dynamics or ''hydrodynamics'', the study of fluid flow *** Computational fluid dynamics, a way of studying fluid dynamics using numerical methods ** Fractional dynamics, dynamics with integrations and differentiations of fractional orders ** Molecular dynamics, the study of motion on the molecular level ** Langevin dynamics, a mathematical model for stochastic dynamics ** Orbital dynamics, the study of the motion of rockets and spacecraft ** Quantum c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacuum Tube
A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type known as a thermionic tube or thermionic valve utilizes thermionic emission of electrons from a hot cathode for fundamental electronic functions such as signal amplifier, amplification and current rectifier, rectification. Non-thermionic types such as a vacuum phototube, however, achieve electron emission through the photoelectric effect, and are used for such purposes as the detection of light intensities. In both types, the electrons are accelerated from the cathode to the anode by the electric field in the tube. The simplest vacuum tube, the diode (i.e. Fleming valve), invented in 1904 by John Ambrose Fleming, contains only a heated electron-emitting cathode and an anode. Electrons can only flow in one direction through the device—fro ... [...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] |
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] |
Plane (mathematics)
In mathematics, a plane is a Euclidean space, Euclidean (flatness (mathematics), flat), two-dimensional surface (mathematics), surface that extends indefinitely. A plane is the two-dimensional analogue of a point (geometry), point (zero dimensions), a line (geometry), line (one dimension) and three-dimensional space. Planes can arise as Euclidean subspace, subspaces of some higher-dimensional space, as with one of a room's walls, infinitely extended, or they may enjoy an independent existence in their own right, as in the setting of two-dimensional Euclidean geometry. Sometimes the word ''plane'' is used more generally to describe a two-dimensional surface (mathematics), surface, for example the hyperbolic plane and elliptic plane. When working exclusively in two-dimensional Euclidean space, the definite article is used, so ''the'' plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graph of a function, graphing are p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science
Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for scientific reasoning is tens of thousands of years old. The earliest written records in the history of science come from Ancient Egypt and Mesopotamia in around 3000 to 1200 BCE. Their contributions to mathematics, astronomy, and medicine entered and shaped Greek natural philosophy of classical antiquity, whereby formal attempts were made to provide explanations of events in the physical world based on natural causes. After the fall of the Western Roman Empire, knowledge of Greek conceptions of the world deteriorated in Western Europe during the early centuries (400 to 1000 CE) of the Middle Ages, but was preserved in the Muslim world during the Islamic Golden Age and later by the efforts of Byzantine Greek scholars who brought Greek ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary information encoded in genes, which can be transmitted to future generations. Another major theme is evolution, which explains the unity and diversity of life. Energy processing is also important to life as it allows organisms to move, grow, and reproduce. Finally, all organisms are able to regulate their own internal environments. Biologists are able to study life at multiple levels of organization, from the molecular biology of a cell to the anatomy and physiology of plants and animals, and evolution of populations.Based on definition from: Hence, there are multiple subdisciplines within biology, each defined by the nature of their research questions and the tools that they use. Like other scientists, biologists use the sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Science
Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". Definition Physical science can be described as all of the following: * A branch of science (a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe)."... modern science is a discovery as well as an invention. It was a discovery that nature generally acts regularly enough to be described by laws and even by mathematics; and required invention to devise the techniques, abstractions, apparatus, and organization for exhibiting the regularities and securing their law-like descriptions." —p.vii, J. L. Heilbron, (2003, editor-in-chief). ''The Oxford Companion to the History of Modern Science''. New York: Oxford University Press. . ** A branch of natural science – natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scholarpedia
''Scholarpedia'' is an English-language wiki-based online encyclopedia with features commonly associated with open-access online academic journals, which aims to have quality content in science and medicine. ''Scholarpedia'' articles are written by invited or approved expert authors and are subject to peer review. ''Scholarpedia'' lists the real names and affiliations of all authors, curators and editors involved in an article: however, the peer review process (which can suggest changes or additions, and has to be satisfied before an article can appear) is anonymous. ''Scholarpedia'' articles are stored in an online repository, and can be cited as conventional journal articles (''Scholarpedia'' has the ISSN number ). ''Scholarpedia''s citation system includes support for revision numbers. The project was created in February 2006 by Eugene M. Izhikevich, while he was a researcher at the Neurosciences Institute, San Diego, California. Izhikevich is also the encyclopedia's editor-i ... [...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] |
Noise (electronic)
In electronics, noise is an unwanted disturbance in an electrical signal. Noise generated by electronic devices varies greatly as it is produced by several different effects. In particular, noise is inherent in physics, and central to thermodynamics. Any conductor with electrical resistance will generate thermal noise inherently. The final elimination of thermal noise in electronics can only be achieved cryogenically, and even then quantum noise would remain inherent. Electronic noise is a common component of noise in signal processing. In communication systems, noise is an error or undesired random disturbance of a useful information signal in a communication channel. The noise is a summation of unwanted or disturbing energy from natural and sometimes man-made sources. Noise is, however, typically distinguished from interference, for example in the signal-to-noise ratio (SNR), signal-to-interference ratio (SIR) and signal-to-noise plus interference ratio (SNIR) meas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is equal to one event per second. The period is the interval of time between events, so the period is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times a minute (2 hertz), the period, —the interval at which the beats repeat—is half a second (60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. Definitions and units For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term ''frequency'' is defined as the number of cycles or vibrations per unit of time. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
