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Moving Equilibrium Theorem
Consider a dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ... (1)..........\dot=f(x,y) (2)..........\qquad \dot=g(x,y) with the state variables x and y. Assume that x is ''fast'' and y is ''slow''. Assume that the system (1) gives, for any fixed y, an asymptotically stable solution \bar(y). Substituting this for x in (2) yields (3)..........\qquad \dot=g(\bar(Y),Y)=:G(Y). Here y has been replaced by Y to indicate that the solution Y to (3) differs from the solution for y obtainable from the system (1), (2). The Moving Equilibrium Theorem suggested by Lotka states that the solutions Y obtainable from (3) approximate the solutions y obtainable from (1), (2) provided the partial system (1) is asymptotically stable in x for any given y and heavily damped (''fast'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamical System
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and 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 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, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geometric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred J
Alfred may refer to: Arts and entertainment *'' Alfred J. Kwak'', Dutch-German-Japanese anime television series * ''Alfred'' (Arne opera), a 1740 masque by Thomas Arne * ''Alfred'' (Dvořák), an 1870 opera by Antonín Dvořák *"Alfred (Interlude)" and "Alfred (Outro)", songs by Eminem from the 2020 album ''Music to Be Murdered By'' Business and organisations * Alfred, a radio station in Shaftesbury, England *Alfred Music, an American music publisher * Alfred University, New York, U.S. * The Alfred Hospital, a hospital in Melbourne, Australia People * Alfred (name) includes a list of people and fictional characters called Alfred * Alfred the Great (848/49 – 899), or Alfred I, a king of the West Saxons and of the Anglo-Saxons Places Antarctica * Mount Alfred (Antarctica) Australia * Alfredtown, New South Wales * County of Alfred, South Australia Canada * Alfred and Plantagenet, Ontario * Alfred Island, Nunavut * Mount Alfred, British Columbia United States * Alfred, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Marshall
Alfred Marshall (26 July 1842 – 13 July 1924) was an English economist, and was one of the most influential economists of his time. His book '' Principles of Economics'' (1890) was the dominant economic textbook in England for many years. It brought the ideas of supply and demand, marginal utility, and costs of production into a coherent whole. He is known as one of the founders of neoclassical economics. Life and career Marshall was born at Bermondsey in London, second son of William Marshall (1812–1901), clerk and cashier at the Bank of England, and Rebecca (1817–1878), daughter of butcher Thomas Oliver, from whom, on her mother's death, she inherited property. William Marshall was a devout strict Evangelical, "author of an Evangelical epic in a sort of Anglo-Saxon language of his own invention which found some favour in its appropriate circles" and of a tract titled ''Men's Rights and Women's Duties''. Marshall had two brothers and two sisters; a cousin was the eco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
