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Bifurcation Memory
Bifurcation memory is a generalized name for some specific features of the behaviour of the dynamical system near the bifurcation. General information The phenomenon is known also under the names of "''stability loss delay for dynamical bifurcations''" and "''ghost attractor''". The essence of the effect of bifurcation memory lies in the appearance of a special type of transition process. An ''ordinary transition process'' is characterized by asymptotic approach of the dynamical system from the state defined by its initial conditions to the state corresponding to its stable stationary regime in the basin of attraction of which the system found itself. However, near the bifurcation boundary can be observed two types of transition processes: passing through the place of the vanished stationary regime, the dynamic system slows down its asymptotic motion temporarily, "as if recollecting the defunct orbit", with the number of revolutions of the phase trajectory in this area of bif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, a dynamical system has a State ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Diagram
In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system. It is usual to represent stable values with a solid line and unstable values with a dotted line, although often the unstable points are omitted. Bifurcation diagrams enable the visualization of bifurcation theory. Logistic map An example is the bifurcation diagram of the logistic map: : x_=rx_n(1-x_n). \, The bifurcation parameter ''r'' is shown on the horizontal axis of the plot and the vertical axis shows the set of values of the logistic function visited asymptotically from almost all initial conditions. The bifurcation diagram shows the forking of the periods of stable orbits from 1 to 2 to 4 to 8 etc. Each of these bifurcation points is a period-doubling bifurcation. The ratio of the lengths of successive intervals between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transition Process
Transition or transitional may refer to: Mathematics, science, and technology Biology * Transition (genetics), a point mutation that changes a purine nucleotide to another purine (A ↔ G) or a pyrimidine nucleotide to another pyrimidine (C ↔ T) * Transitional fossil, any fossilized remains of a lifeform that exhibits the characteristics of two distinct taxonomic groups * A phase during childbirth contractions during which the cervix completes its dilation Gender and sex * Gender transitioning, the process of changing one's gender presentation to accord with one's internal sense of one's gender – the idea of what it means to be a man or woman * Sex reassignment therapy, the physical aspect of a gender transition Physics * Phase transition, a transformation of the state of matter; for example, the change between a solid and a liquid, between liquid and gas or between gas and plasma * Quantum phase transition, a phase transformation between different quantum phases * Quantu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lev Pontryagin
Lev Semenovich Pontryagin (russian: Лев Семёнович Понтрягин, also written Pontriagin or Pontrjagin) (3 September 1908 – 3 May 1988) was a Soviet mathematician. He was born in Moscow and lost his eyesight completely due to an unsuccessful eye surgery after a primus stove explosion when he was 14. Despite his blindness he was able to become one of the greatest mathematicians of the 20th century, partially with the help of his mother Tatyana Andreevna who read mathematical books and papers (notably those of Heinz Hopf, J. H. C. Whitehead, and Hassler Whitney) to him. He made major discoveries in a number of fields of mathematics, including optimal control, algebraic topology and differential topology. Work Pontryagin worked on duality theory for homology while still a student. He went on to lay foundations for the abstract theory of the Fourier transform, now called Pontryagin duality. With René Thom, he is regarded as one of the co-founders of cobordism ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ship
A ship is a large watercraft that travels the world's oceans and other sufficiently deep waterways, carrying cargo or passengers, or in support of specialized missions, such as defense, research, and fishing. Ships are generally distinguished from boats, based on size, shape, load capacity, and purpose. Ships have supported exploration, trade, warfare, migration, colonization, and science. After the 15th century, new crops that had come from and to the Americas via the European seafarers significantly contributed to world population growth. Ship transport is responsible for the largest portion of world commerce. The word ''ship'' has meant, depending on the era and the context, either just a large vessel or specifically a ship-rigged sailing ship with three or more masts, each of which is square-rigged. As of 2016, there were more than 49,000 merchant ships, totaling almost 1.8 billion dead weight tons. Of these 28% were oil tankers, 43% were bulk carriers, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coagulation
Coagulation, also known as clotting, is the process by which blood changes from a liquid to a gel, forming a blood clot. It potentially results in hemostasis, the cessation of blood loss from a damaged vessel, followed by repair. The mechanism of coagulation involves activation, adhesion and aggregation of platelets, as well as deposition and maturation of fibrin. Coagulation begins almost instantly after an injury to the endothelium lining a blood vessel. Exposure of blood to the subendothelial space initiates two processes: changes in platelets, and the exposure of subendothelial tissue factor to plasma factor VII, which ultimately leads to cross-linked fibrin formation. Platelets immediately form a plug at the site of injury; this is called ''primary hemostasis. Secondary hemostasis'' occurs simultaneously: additional coagulation (clotting) factors beyond factor VII ( listed below) respond in a cascade to form fibrin strands, which strengthen the platelet plug. Disorders of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Myocardium
Cardiac muscle (also called heart muscle, myocardium, cardiomyocytes and cardiac myocytes) is one of three types of vertebrate muscle tissues, with the other two being skeletal muscle and smooth muscle. It is an involuntary, striated muscle that constitutes the main tissue of the wall of the heart. The cardiac muscle (myocardium) forms a thick middle layer between the outer layer of the heart wall (the pericardium) and the inner layer (the endocardium), with blood supplied via the coronary circulation. It is composed of individual cardiac muscle cells joined by intercalated discs, and encased by collagen fibers and other substances that form the extracellular matrix. Cardiac muscle contracts in a similar manner to skeletal muscle, although with some important differences. Electrical stimulation in the form of a cardiac action potential triggers the release of calcium from the cell's internal calcium store, the sarcoplasmic reticulum. The rise in calcium causes the cell's m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tachycardia
Tachycardia, also called tachyarrhythmia, is a heart rate that exceeds the normal resting rate. In general, a resting heart rate over 100 beats per minute is accepted as tachycardia in adults. Heart rates above the resting rate may be normal (such as with exercise) or abnormal (such as with electrical problems within the heart). Complications Tachycardia can lead to fainting. When the rate of blood flow becomes too rapid, or fast blood flow passes on damaged endothelium, it increases the friction within vessels resulting in turbulence and other disturbances. According to the Virchow's triad, this is one of the three conditions that can lead to thrombosis (i.e., blood clots within vessels). Causes Some causes of tachycardia include: * Adrenergic storm * Anaemia * Anxiety * Atrial fibrillation * Atrial flutter * Atrial tachycardia * Atrioventricular reentrant tachycardia * AV nodal reentrant tachycardia * Brugada syndrome * Circulatory shock and its various causes ( obstr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardiophysics
Cardiophysics is an interdisciplinary science that stands at the junction of cardiology and medical physics, with researchers using the methods of, and theories from, physics to study cardiovascular system at different levels of its organisation, from the molecular scale to whole organisms. Being formed historically as part of systems biology, ''cardiophysics'' designed to reveal connections between the physical mechanisms, underlying the organization of the cardiovascular system, and biological features of its functioning. Zbigniew R. Struzik seems to be a first author who used the term in a scientific publication in 2004. One can use interchangeably also the terms ''cardiovascular physics''. See also * Medical physics * Important publications in medical physics * Biomedicine * Biomedical engineering * Physiome * Nanomedicine References * Books *# *# *# * Papers *# *# *# *# *# *# *# External links * Bioelectric Information Processing Laboratory of thInstit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation (other)
Bifurcation or bifurcated may refer to: Science and technology * Bifurcation theory, the study of sudden changes in dynamical systems ** Bifurcation, of an incompressible flow, modeled by squeeze mapping the fluid flow * River bifurcation, the forking of a river into its tributaries * Bifurcation lake, a lake that flows into two different drainage basins * Bifurcated bonding, a single hydrogen atom participates in two hydrogen bonds Other uses * Bifurcation (law), the division of issues in a trial See also * Aortic bifurcation, the point at which the abdominal aorta bifurcates into the left and right common iliac arteries * Tracheal bifurcation, or the carina of trachea (Latin: ''bifurcatio tracheae'') * Bifurcation diagram * Bifurcate merging, a kinship system * False dilemma or bifurcation * Tongue bifurcation (other) * Fork (other) A fork is a utensil for eating and cooking. Fork may also refer to: Implements * Fork (road), a type of intersection where a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bifurcation Theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps). The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior. Henri Poincaré also later named various types of stationary points and classified them . Bifurcation types It is useful to divide bifurcations into two principal classes: * Local bifurcations, which can b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Portrait
A phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane. Each set of initial conditions is represented by a different curve, or point. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the state space. This reveals information such as whether an attractor, a repellor or limit cycle is present for the chosen parameter value. The concept of topological equivalence is important in classifying the behaviour of systems by specifying when two different phase portraits represent the same qualitative dynamic behavior. An attractor is a stable point which is also called "sink". The repeller is considered as an unstable point, which is also known as "source". A phase portrait graph of a dynamical system depicts the system's trajectories (with arrows) and stable steady states (with dots) and unstable steady states (with circles) in a state space. The axes are of st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
