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Pyragas Method
In the mathematics of chaotic dynamical systems, in the Pyragas method of stabilizing a periodic orbit In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time. Iterated functions Given ..., an appropriate continuous controlling signal is injected into the system, whose intensity is nearly zero as the system evolves close to the desired periodic orbit but increases when it drifts away from the desired orbit. Both the Pyragas and OGY ( Ott, Grebogi and Yorke) methods are part of a general class of methods called "closed loop" or "feedback" methods which can be applied based on knowledge of the system obtained through solely observing the behavior of the system as a whole over a suitable period of time. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaotic Dynamical System
Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sensitive to initial conditions. These 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 there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause or prevent a tornado in Texas. Text was copied from this source, which is avai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Orbit
In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time. Iterated functions Given a mapping from a set into itself, :f: X \to X, a point in is called periodic point if there exists an >0 so that :\ f_n(x) = x where is the th iterate of . The smallest positive integer satisfying the above is called the ''prime period'' or ''least period'' of the point . If every point in is a periodic point with the same period , then is called ''periodic'' with period (this is not to be confused with the notion of a periodic function). If there exist distinct and such that :f_n(x) = f_m(x) then is called a preperiodic point. All periodic points are preperiodic. If is a diffeomorphism of a differentiable manifold, so that the derivative f_n^\prime is defined, then one says that a periodic point is ''hyperbolic'' if :, f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Ott
Edward Ott (born 22 December 1941) is an American physicist and electrical engineer, who is a professor at University of Maryland, College Park. He is best known 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 ... [...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 may refer to: People * James (given name) * James (surname) * James (musician), aka Faruq Mahfuz Anam James, (born 1964), Bollywood musician * James, brother of Jesus * King James (other), various kings named James * Prince James (other) * Saint James (other) Places Canada * James Bay, a large body of water * James, Ontario United Kingdom * James College, York, 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 Film and television * James (2005 film), ''James'' (2005 film), a Bollywood film * James (2008 film), ''James'' (2008 film), an Irish short film * James (2022 film), ''James'' (2022 film), an Indian Kannada-language film * "James", a television Adventure Time (season 5)#ep42, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lithuanians
Lithuanians () are a Balts, Baltic ethnic group. They are native to Lithuania, where they number around 2,378,118 people. Another two million make up the Lithuanian diaspora, largely found in countries such as the Lithuanian Americans, United States, Lithuanians in the United Kingdom, United Kingdom, Lithuanian Brazilians, Brazil and Lithuanian Canadians, Canada. Their native language is Lithuanian language, Lithuanian, one of only two surviving members of the Baltic language family along with Latvian language, Latvian. According to the Lithuanian census of 2021, census conducted in 2021, 84.6% of the population of Lithuania identified themselves as Lithuanians. Most Lithuanians belong to the Catholic Church in Lithuania, Catholic Church, while the Lietuvininkai who lived in the northern part of East Prussia prior to World War II, were mostly Lutherans. History The territory of the Balts, including modern Lithuania, was once inhabited by several Baltic tribal entities (Sudovi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chaos Theory
Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sensitive to initial conditions. These 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 there is sensitive dependence on initial conditions). A metaphor for this behavior is that a butterfly flapping its wings in Brazil can cause or prevent a tornado in Texas. Text was copied from this source, which is avai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
