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Control Of Chaos
In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. Any chaotic attractor contains an infinite number of unstable, periodic orbits. Chaotic dynamics, then, consists of a motion where the system state moves in the neighborhood of one of these orbits for a while, then falls close to a different unstable, periodic orbit where it remains for a limited time and so forth. This results in a complicated and unpredictable wandering over longer periods of time. Control of chaos is the stabilization, by means of small system perturbations, of one of these unstable periodic orbits. The result is to render an otherwise chaotic motion more stable and predictable, which is often an advantage. The perturbation must be tiny compared to the overall size of the attractor of the system to avoid significant modification of the system's natural dynamics. Several techniques have been devised for chaos control, but most are de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Experiment
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experiment, natural experimental studies. A child may carry out basic experiments to understand how things fall to the ground, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of hands-on activities are very important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning, especially when used over time. Experiments can vary from personal and in ... [...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 roundin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Attractor
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed. In finite-dimensional systems, the evolving variable may be represented algebraically as an ''n''-dimensional vector. The attractor is a region in ''n''-dimensional space. In physical systems, the ''n'' dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate. If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imperial College Press
Imperial College Press (ICP) was formed in 1995 as a partnership between Imperial College of Science, Technology and Medicine in London and World Scientific publishing. This publishing house was awarded the rights, by The Nobel Foundation, Sweden, to publish ''The Nobel Prize: The First 100 years'', edited by Agneta Wallin Levinovitz and Nils Ringertz. They publish areas of teaching and research at Imperial College: Chemistry, Computer Science, Economics, Finance & Management, Engineering, Environmental Science, Life Sciences, Mathematics, Medicine & Healthcare, and Physics. As of August 2016, ICP has been fully incorporated into World Scientific under the new imprint, ''World Scientific Europe''. Selected journals * ''Journal of Bioinformatics and Computational Biology'' * ''Journal of Integrative Neuroscience'' * ''International Journal of Innovation Management'' * ''Journal of Environmental Assessment Policy and Management A journal, from the Old French ''journal'' ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eckehard Schöll
Eckehard Schöll (born 6 February 1951 in Stuttgart, Germany) is a German physicist and mathematician as well as a Professor of theoretical physics at the Technical University of Berlin. He is an expert in the field of nonlinear dynamics and head of the group Nonlinear dynamics and control. His work pertains to research in the fields of mathematics and physics, particularly semiconductor physics, neurodynamics and bifurcation theory. His latest research is also related to topics in biology and the social sciences, e.g. simulation of the dynamics in socioeconomic or neuronal networks. He is one of the forerunners into the research of chimera states. Eckehard Schöll is the author of over 500 publications in scientific journals, three books (''Nonequilibrium Phase Transitions in Semiconductors'' (Springer 1987), ''The Physics of Instabilities in Solid State Electron Devices'' (Plenum Press, New York, 1992), and ''Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiley-VCH
Wiley-VCH is a German publisher owned by John Wiley & Sons. It was founded in 1921 as Verlag Chemie (meaning "Chemistry Press": VCH stands for ''Verlag Chemie'') by two German learned societies. Later, it was merged into the German Chemical Society The German Chemical Society (German: ', GDCh) is a learned society and professional association founded in 1949 to represent the interests of German chemists in local, national and international contexts. GDCh "brings together people working in ch ... (GDCh). In 1991, VCH acquired Akademie Verlag. It has been owned by John Wiley & Sons since 1996. The humanities section of Akademie Verlag and the Akademie brand were sold in 1997 to R. Oldenbourg Verlag, while VCH retained the natural sciences catalog. References External links * Wiley (publisher) Publishing companies of Germany Publishing companies established in 1921 Weinheim German companies established in 1921 {{publish-company-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Ott
Edward Ott (born 22 December 1941) is an American physicist most noted for his contributions to the development of chaos theory. Ott was born and grew up in New York City. He attended Stuyvesant High School, received his bachelor's degree in Electrical Engineering from The Cooper Union, and his Ph.D. in Electrophysics from The Polytechnic Institute of Brooklyn in 1967. Following receipt of his Ph.D. he was an NSF postdoctoral fellow in the Department of Applied Mathematics and Theoretical Physics of Cambridge University. He then joined the faculty of the Department of Electrical Engineering at Cornell University. Since 1979 he has been a faculty member jointly in the Department of Physics and the Department of Electrical Engineering at The University of Maryland, with the current titles of Distinguished University Professor, and Yuen Sang and Yuen Kit So Professor. He was elected to the National Academy of Sciences in 2022. Research areas Prior to his work on chaos and compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Celso Grebogi
Celso Grebogi (born 1947) is a Brazilian theoretical physicist who works in the area of chaos theory. He is one among the pioneers in the nonlinear and complex systems and chaos theory. Currently he works at the University of Aberdeen as the "Sixth Century Chair in Nonlinear and Complex Systems". He has done extensive research in the field of plasma physics before his work on the theory of dynamical systems. He and his colleagues ( Edward Ott and James A. Yorke) have shown with a numerical example that one can convert a chaotic attractor to any one of numerous possible attracting time-periodic motions by making only small time-dependent perturbations of an available system parameter. This article is considered as one among the classic works in the control theory of chaos and their control method is known as the OGY method. He was listed in the 2016 Thomson Reuters Citation Laureates. Research areas Grebogi has worked in the fields of dynamics of nonlinear and complex systems i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James A
James is a common English language surname and given name: * James (name), the typically masculine first name James * James (surname), various people with the last name James James or James City may also refer to: People * King James (other), various kings named James * Saint James (other) * James (musician) * James, brother of Jesus Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, a college of the University of York United States * James, Georgia, an unincorporated community * James, Iowa, an unincorporated community * James City, North Carolina * James City County, Virginia ** James City (Virginia Company) ** James City Shire * James City, Pennsylvania * St. James City, Florida Arts, entertainment, and media * ''James'' (2005 film), a Bollywood film * ''James'' (2008 film), an Irish short film * ''James'' (2022 film), an Indian Kannada-language film * James the Red Engine, a character in ''Thomas the Tan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poincaré Section
Poincaré is a French surname. Notable people with the surname include: * Henri Poincaré (1854–1912), French physicist, mathematician and philosopher of science * Henriette Poincaré (1858-1943), wife of Prime Minister Raymond Poincaré * Lucien Poincaré (1862–1920), physicist, brother of Raymond and cousin of Henri * Raymond Poincaré (1860–1934), French Prime Minister or President ''inter alia'' from 1913 to 1920, cousin of Henri See also *List of things named after Henri Poincaré In physics and mathematics, a number of ideas are named after Henri Poincaré: * Euler–Poincaré characteristic * Hilbert–Poincaré series * Poincaré–Bendixson theorem * Poincaré–Birkhoff theorem * Poincaré–Birkhoff–Witt theorem, u .... * * {{DEFAULTSORT:Poincare French-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchronization Of Chaos
Synchronization of chaos is a phenomenon that may occur when two or more dissipative chaotic systems are coupled. Because of the exponential divergence of the nearby trajectories of chaotic systems, having two chaotic systems evolving in synchrony might appear surprising. However, synchronization of coupled or driven chaotic oscillators is a phenomenon well established experimentally and reasonably well-understood theoretically. The stability of synchronization for coupled systems can be analyzed using master stability. Synchronization of chaos is a rich phenomenon and a multi-disciplinary subject with a broad range of applications. Synchronization may present a variety of forms depending on the nature of the interacting systems and the type of coupling, and the proximity between the systems. Identical synchronization This type of synchronization is also known as complete synchronization. It can be observed for identical chaotic systems. The systems are said to be completely s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synchronization
Synchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are said to be synchronous or ''in sync''—and those that are not are '' asynchronous''. Today, time synchronization can occur between systems around the world through satellite navigation signals and other time and frequency transfer techniques. Navigation and railways Time-keeping and synchronization of clocks is a critical problem in long-distance ocean navigation. Before radio navigation and satellite-based navigation, navigators required accurate time in conjunction with astronomical observations to determine how far east or west their vessel traveled. The invention of an accurate marine chronometer revolutionized marine navigation. By the end of the 19th century, important ports provided time signals in the form of a signal gun, flag, or dropping ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
