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Nikolay V. Kuznetsov
Nikolay Vladimirovich Kuznetsov (russian: Николай Владимирович Кузнецов; born 13 May 1979 in Leningrad, Soviet Union, USSR) is a specialist in nonlinear dynamics and control theory. Academic career He graduated from the Saint Petersburg State University, St. Petersburg University, Department of Theoretical Cybernetics chaired by Vladimir Yakubovich, V.A. Yakubovich, in 2001. In 2004 he received Candidate of Science degree (supervisor Gennady Leonov, G.A. Leonov) and in 2016 Doctor of Science degree (Habilitation) from St. Petersburg University. From 2003 Nikolay Kuznetsov has been working in St. Petersburg University and now he is Full professor (tenured) and Head of the Department of Applied Cybernetics there. Since 2018 the research group chaired by Kuznetsov has been awarded the status of Center of excellence#Russia, the Leading Scientific School (Center of Excellence) of Russia in the field of mathematics and mechanics. In 2020 he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eden’s Conjecture
In the mathematics of dynamical systems, Eden's conjecture states that the supremum of the local Lyapunov dimensions on the global attractor is achieved on a stationary point or an unstable periodic orbit embedded into the attractor. The validity of the conjecture was proved for a number of well-known systems having global attractor (e.g. for the global attractors in the Lorenz system, complex Ginzburg–Landau equation). It is named after Alp Eden, who proposed it in 1987. Kuznetsov–Eden's conjecture For local attractors, a ''conjecture on the Lyapunov dimension of self-excited attractor'', refined by N. Kuznetsov, is stated that for a typical system, the Lyapunov dimension of a self-excited attractor does not exceed the Lyapunov dimension of one of the unstable equilibria, the unstable manifold of which intersects with the basin of attraction and visualizes the attractor. The conjecture is valid, e.g., for the classical self-excited Lorenz attractor; for the self-e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov Dimension
In the mathematics of dynamical systems, the concept of Lyapunov dimension was suggested by Kaplan and Yorke for estimating the Hausdorff dimension of attractors. Further the concept has been developed and rigorously justified in a number of papers, and nowadays various different approaches to the definition of Lyapunov dimension are used. Remark that the attractors with noninteger Hausdorff dimension are called strange attractors. Since the direct numerical computation of the Hausdorff dimension of attractors is often a problem of high numerical complexity, estimations via the Lyapunov dimension became widely spread. The Lyapunov dimension was named after the Russian mathematician Aleksandr Lyapunov because of the close connection with the Lyapunov exponents. Definitions Consider a dynamical system \big(\_, (U\subseteq \mathbb^n, \, \cdot\, )\big) , where \varphi^t is the shift operator along the solutions: \varphi^t(u_0) = u(t,u_0), of ODE \dot = f(), t \leq 0, or differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gennady Leonov
Gennady Alexeyevich Leonov (russian: Геннадий Алексеевич Леонов; February 2, 1947Russian Academy of Sciences (in Russian) in Leningrad, Soviet Union – April 23, 2018) was a Russian scientist, Correspondent Member of the Russian Academy of Sciences (since 2006), Professor at the Saint Petersburg State University, Doktor nauk, Doctor of Sciences. Laureate of the 1986 USSR State Prize and 2012 Aleksandr Andronov Russian Academy of Sciences Prize. He graduated from the Leningrad State University in 1969. In 1971 he defended his Candidate_of_Sciences, Candidate's Dissertation. In 1983 he defended his doctoral dissertation. In 1986 he received the title of Professor. Since 1988, he served as Dean of the Faculty of Mathematics and Me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Petersburg
Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), is the second-largest city in Russia. It is situated on the Neva River, at the head of the Gulf of Finland on the Baltic Sea, with a population of roughly 5.4 million residents. Saint Petersburg is the fourth-most populous city in Europe after Istanbul, Moscow and London, the most populous city on the Baltic Sea, and the world's northernmost city of more than 1 million residents. As Russia's Imperial capital, and a historically strategic port, it is governed as a federal city. The city was founded by Tsar Peter the Great on 27 May 1703 on the site of a captured Swedish fortress, and was named after apostle Saint Peter. In Russia, Saint Petersburg is historically and culturally associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finnish Academy Of Science And Letters
The Finnish Academy of Science and Letters (Finnish ''Suomalainen Tiedeakatemia''; Latin ''Academia Scientiarum Fennica'') is a Finnish learned society. It was founded in 1908 and is thus the second oldest academy in Finland. The oldest is the Finnish Society of Sciences and Letters, which was founded in 1838. Members The academy has a total of 328 seats for Finnish members. When a member of the academy turns 65 years, his seat is free for selection of a new member, but he remains a full member until death. The seats are divided into two sections Section of Science * Mathematics and Computer Science 28 members * Physics and Astronomy 26 members * Geosciences 24 members * Chemistry 21 members * Biology 22 members * Agriculture and Forestry 22 members * Medicine 46 members 189 seats Section of the Humanities * Theology and Religion 11 members * Philosophy and Aesthetics 12 members * Psychology and Pedagogy 14 members * History and Archaeology 17 members * Finno-Ugric Studi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyapunov Exponent
In mathematics, the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories. Quantitatively, two trajectories in phase space with initial separation vector \delta \mathbf_0 diverge (provided that the divergence can be treated within the linearized approximation) at a rate given by : , \delta\mathbf(t) , \approx e^ , \delta \mathbf_0 , where \lambda is the Lyapunov exponent. The rate of separation can be different for different orientations of initial separation vector. Thus, there is a spectrum of Lyapunov exponents—equal in number to the dimensionality of the phase space. It is common to refer to the largest one as the maximal Lyapunov exponent (MLE), because it determines a notion of predictability for a dynamical system. A positive MLE is usually taken as an indication that the system is chaotic (provided some other conditions are met, e.g., phase space comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalman's Conjecture
Kalman's conjecture or Kalman problem is a disproved conjecture on absolute stability of nonlinear control system with one scalar nonlinearity, which belongs to the sector of linear stability. Kalman's conjecture is a strengthening of Aizerman's conjecture and is a special case of Markus–Yamabe conjecture. This conjecture was proven false but led to the (valid) sufficient criteria on absolute stability. Mathematical statement of Kalman's conjecture (Kalman problem) In 1957 R. E. Kalman in his paper stated the following: If ''f''(''e'') in Fig. 1 is replaced by constants ''K'' corresponding to all possible values of ''f'''(''e''), and it is found that the closed-loop system is stable for all such ''K'', then it intuitively clear that the system must be monostable; i.e., all transient solutions will converge to a unique, stable critical point. Kalman's statement can be reformulated in the following conjecture: Consider a system with one scalar nonlinearity'' : \fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Describing Function
In control systems theory, the describing function (DF) method, developed by Nikolay Mitrofanovich Krylov and Nikolay Bogoliubov in the 1930s, and extended by Ralph Kochenburger is an approximate procedure for analyzing certain nonlinear control problems. It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by a linear time-invariant (LTI) transfer function that depends on the amplitude of the input waveform. By definition, a transfer function of a true LTI system cannot depend on the amplitude of the input function because an LTI system is linear. Thus, this dependence on amplitude generates a family of linear systems that are combined in an attempt to capture salient features of the non-linear system behavior. The describing function is one of the few widely applicable methods for designing nonlinear systems, and is very widely used as a standard mathematical tool for analyzing limit cycles in closed-loop controllers, such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CP-PLL
Charge-pump phase-locked loop (CP-PLL) is a modification of phase-locked loop A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a ...s with phase-frequency detector and square waveform signals. CP-PLL allows for a quick lock of the phase of the incoming signal, achieving low steady state phase error. Phase-frequency detector (PFD) Phase-frequency detector (PFD) is triggered by the trailing edges of the reference (Ref) and controlled (VCO) signals. The output signal of PFD i(t) can have only three states: 0, +I_p, and -I_p. A trailing edge of the reference signal forces the PFD to switch to a higher state, unless it is already in the state +I_p. A trailing edge of the VCO signal forces the PFD to switch to a lower state, unless it is already in the state -I_p. If both trailing edges ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floyd M
Floyd may refer to: As a name * Floyd (given name), a list of people and fictional characters * Floyd (surname), a list of people and fictional characters Places in the United States * Floyd, Arkansas, an unincorporated community * Floyd, Iowa, a city in Floyd County * Floyd, Ray County, Missouri, an unincorporated community * Floyd, Washington County, Missouri, an unincorporated community * Floyd, New Mexico, a village * Floyd, New York, a town * Floyd, Texas, an unincorporated community * Floyd, Virginia, a town in Floyd County * Floyd County (other) * Floyd River, Iowa, a tributary of the Missouri River * Floyd Township (other) * Camp Floyd / Stagecoach Inn State Park and Museum, a short-lived U.S. Army post near Fairfield, Utah * Floyd's Bluff, a hill near Sioux City, Iowa Storms * Hurricane Floyd, major hurricane of 1999 * Tropical Storm Floyd (other), for other storms named Floyd Sports * Floyd (horse), a National Hunt racehorse * Fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
:en:William F
William is a masculine given name of Norman French origin.Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 276. It became very popular in the English language after the Norman conquest of England in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will, Wills, Willy, Willie, Liam, Bill, and Billy. A common Irish form is Liam. Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie or the play ''Douglas''). Female forms are Willa, Willemina, Wilma and Wilhelmina. Etymology William is related to the German given name ''Wilhelm''. Both ultimately descend from Proto-Germanic ''*Wiljahelmaz'', with a direct cognate also in the Old Norse name ''Vilhjalmr'' and a West Germanic borrowing into Medieval Latin ''Willelmus''. The Proto-Germanic name is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sommerfeld Effect
In mechanics, Sommerfeld effect is a phenomenon arising from feedback in the energy exchange between vibrating systems: for example, when for the rocking table, under given conditions, energy transmitted to the motor resulted not in higher revolutions but in stronger vibrations of the table. It is named after Arnold Sommerfeld. In 1902, A. Sommerfeld analyzed the vibrations caused by a motor driving an unbalanced weight and wrote that "''This experiment corresponds roughly to the case in which a factory owner has a machine set on a poor foundation running at 30 horsepower. He achieves an effective level of just 1/3, however, because only 10 horsepower are doing useful work, while 20 horsepower are transferred to the foundational masonry''". First mathematical descriptions of Sommerfeld effect were suggested by I. Blekhman and V. Konenko. Hidden attractors in Sommerfeld effect In the theory of hidden oscillations, Sommerfeld effect is explained by the multistability and presence in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
