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# Topic: Nonlinear systems

###### In the News (Sun 21 Jul 19)

 Nonlinear Dynamics and Complex Systems Theory (Glossary)   (Site not responding. Last check: 2007-11-05) Dissipative systems are dynamical systems that are characterized by some sort of "internal friction" that tends to contract phase space volume elements. If f is a nonlinear function or an operator, and x is a system input (either a function or variable), then the effect of adding two inputs, x1 and x2, first and then operating on their sum is, in general, not equivalent to operating on two inputs separately and then adding the outputs together; i.e. Consider a complex system (that is, a system composed of many individual parts) that is controlled from the outside in some manner by a control parameter (say, the system is driven by a constant influx of energy and/or matter). www.cna.org /isaac/Glossb.htm   (8567 words)

 Cornell NSF-IGERT The subject of nonlinear systems is wonderfully broad and has important applications in fields ranging from physics, mechanical engineering and computer science to the life sciences, sociology and finance. A mathematics student studying dynamical systems, a physiologist studying the heart and a computer scientist studying the internet are all studying nonlinear phenomena. In contrast, the Nonlinear Systems Program brings together doctoral candidates enrolled in diverse graduate fields for broad multidisciplinary training in nonlinear systems early in their graduate careers. www.chaos.cornell.edu   (373 words)

 Nonlinear Systems Laboratory Homepage Lohmiller, W., and Slotine, J.J.E., "Contraction Analysis for Nonlinear Systems," Automatica, 34(6), 1998. Slotine, J.J.E., Hedrick, J.K., and Misawa, E., "On Sliding Observers for Nonlinear Systems," A.S.M.E. Dynamic Systems, Measurement, and Control, 109(3), 1987. "On Metric Observers for Nonlinear Systems," IEEE Int. web.mit.edu /afs/athena.mit.edu/org/n/nsl/www   (1115 words)

 Nonlinear Programming FAQ MathOptimizer, for global and local (numerical) solution of a very general class of nonlinear optimization problems defined by a finite number of real-valued, continuous functions over a finite n-dimensional interval region; intended particularly for dense, highly nonlinear systems, including those that have a (typically unknown) number of local optima. Global Optimization is a collection of functions for global nonlinear optimization that uses the Mathematica system as an interface for defining the nonlinear system to be solved and for computing function numeric values. Nonlinear problems are accepted in the form of a C or Fortran program or in modeling languages such as AMPL and GAMS. www-unix.mcs.anl.gov /otc/Guide/faq/nonlinear-programming-faq.html   (5827 words)

 Nonlinear Control Abstracts For general nonlinear systems, it is shown that one of the new properties is strictly weaker than ISS, while the other one is equivalent to it. Moreover, it is established that, for general nonlinear control systems under persistently acting disturbances, the existence of smooth Lyapunov functions is equivalent to the existence of (possibly) discontinuous) feedback stabilizers which are robust with respect to small measurement errors and small additive external disturbances. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. www.math.rutgers.edu /~sontag/NCA   (8904 words)

 Nonlinear Dynamical Systems (NLDS) @ San Diego State The Theory of Dynamical Systems is the paradigm for modeling and studying phenomena that undergo spatial and temporal evolution. In recent years, thanks to the advent of powerful computers and the Theory of Dynamical Systems, it is now possible to tackle, at some extent, nonlinear systems. After all, nonlinearity is at the heart of most of the interesting dynamics. nlds.sdsu.edu   (1293 words)

 Nonlinear Science FAQ   (Site not responding. Last check: 2007-11-05) Nonlinear is defined as the negation of linear. System: Requires Windows 95, at least 256 colours Available : http://www.fssc.demon.co.uk/rdiffusion/ilya.htm INSITE (It's a Nonlinear Systems Investigative Toolkit for Everyone) is a collection for the simulation and characterization of dynamical systems, with an emphasis on chaotic systems. System: Comes as C source, Fortran source, PC executable, etc Available: http://www.cooper.edu/engineering/physics/wolf/ (Seems to be missing?) Lyapunov Exponents and Time Series Michael Banbrook's C codes for Lyapunov exponents and time series analysis System: Sun with X windows. www.faqs.org /faqs/sci/nonlinear-faq   (11552 words)

 Nonlinear Systems Most of real life problems involve nonlinear systems (predator-prey model is one such example). The nonlinear system are very hard to solve explicitly but qualitative and numerical techniques may help shade some information on the behavior of the solutions. The main idea is to approximate a nonlinear system by a linear one hoping that the conclusions on one will be the same as the other one. www.sosmath.com /diffeq/system/nonlinear/nonlinear.html   (132 words)

 Nonlinear Phenomena in Complex Systems - Online Journal The primary objective of Nonlinear Phenomena in Complex Systems (NPCS) is to provide a single forum for this interdisciplinary area to strengthen links between basic and applied research, theoretical and experimental methods relating to nonlinear dynamics of complex systems encountered in the natural and social sciences. Its goal is to bring together, in one periodical, significant papers of high quality on all aspects of nonlinear dynamics, including phenomena, modelling, and complexity, thereby providing a focus and catalyst for the timely dissemination and cross-fertilization of new ideas, principles, and techniques across a broad interdisciplinary front. Nonlinear Phenomena in Complex Systems is a quarterly journal, which publishes original research papers and reviews. www.j-npcs.org   (461 words)

 Systems Recently, the connections between piecewise linear control systems and adaptive controllers have been studied, with the pourpose of showing the relevance of adaptive techniques for the control of nonlinear systems. Developing a convenient stochastic calculus, it has been shown that the Brownian motion of a particle, in an external force field and under the assumption of thermic equilibrium, satisfies a principle which is analogous to the Hamilton principle in classical mechanics (Pavon [1986]). Linear filters of minimal dimension for finite state systems are studied in Di Masi, Kitsul a nd Liptser [1991]. www.ladseb.pd.cnr.it /control/control.html   (1976 words)

 Nonlinear Systems and Chaos at Ohio U. Most natural phenomena are nonlinear ; yet even today, theoretical analysis of physical systems is usually based on linear mathematical models or ones having small deviations from linearity. Thus, systems as diverse as a dripping faucet and a heart in ventricular fibrillation show many common features in their dynamics. Some of these techniques were applied to experiments including systems of up to 32 coupled diode resonators showing spatio-temporal chaos and an electro-chemical cell operating in a highly nonlinear regime where spontaneous oscillations and chaos are observed. www.phy.ohiou.edu /research/cmss/chaos.html   (469 words)

 CDC2000 Nonlinear Dynamical Systems   (Site not responding. Last check: 2007-11-05) Under appropriate conditions, the solutions of a time-varying system with disturbances are shown to converge uniformly on compact time intervals to the solutions of the system's average as the rate of change of time increases to infinity. We consider approximating systems obtained by replacing this non-Lipschitzian relation with a Lipschitzian function and investigate the convergence of the solutions of the approximating system to those of the ideal system as the Lipschitzian characteristic approaches to the (non-Lipschitzian) complementarity relation. The proposed approach to analysis of nonlinear systems is based on excitability index - a nonlinear counterpart of magnitude frequency response of linear system. www.mm.anadolu.edu.tr /ieeecss/39cdc/CD00S17E.HTM   (851 words)

 Sci.Nonlinear FAQ 2.0 (Sept 2003) - [3] Applications and Advanced Theory   (Site not responding. Last check: 2007-11-05) Complex systems are spatially and/or temporally extended nonlinear systems characterized by collective properties associated with the system as a whole--and that are different from the characteristic behaviors of the constituent parts. This is the application of dynamical systems techniques to a data series, usually obtained by "measuring" the value of a single observable as a function of time. It was expected that a typical perturbation of an integrable Hamiltonian system would lead to "ergodic" motion, a weak version of chaos in which all of phase space is covered, but the Lyapunov exponents [2.11] are not necessarily positive. amath.colorado.edu /faculty/jdm/faq-[3].html   (4382 words)

 Nonlinear Iterated Function Systems   (Site not responding. Last check: 2007-11-05) Nonlinear functions are defined (in analogy to the above approach for affine functions) by grid distortions. Above an interactive program for the specification of 2D linear and nonlinear Iterated Function Systems is shown. An LR-table controls the application of individual functions during the "stochastic algorithm" that is used for fast visualization of the fractal limit set. www.cg.tuwien.ac.at /research/vis-dyn-syst/nifs/nlinifs.html   (361 words)

 Nonlinear Systems Analysis   (Site not responding. Last check: 2007-11-05) For further reading: Nonlinear systems (2nd edition) by H. Khalil, published by Prentice-Hall, ISBN is 0-13-228024-8. The main difference from the course Introduction to Nonlinear ControlSystems is: in that course, the synthesis or control design of nonlinear control systems is emphasized; and in this course, the analysis tools are studied. we plan to cover a range of topics on nonlinear systems such as approximation methods, periodic solutions, Liapunov stability, input-output stability and nonsmooth systems. www.math.kth.se /~hu/5B5770.html   (295 words)

 Complex Systems Homepage Listing The Center for Interdisciplinary Research on Complex Systems -The CIRCS was created as a result of the present challenges in conducting quantitative interdisciplinary research on the most important problems in biology and materials science, with strong components in modern microfabrication and large scale computer simulations. The Center For Nonlinear Studies - University of Leeds - The CNLS was established at the University of Leeds in 1984 to enhance existing and foster new research collaborations between mathematicians, scientists and engineers throughout the campus, with a common interest in nonlinear dynamics and its applications. The Centre for Complex Systems -The overarching objective of the Center is to understand the mechanisms and principles underlying complex behavior on all levels, from molecules and cells to whole brain functioning. www.ceptualinstitute.com /genre/NCSLdirectory.htm   (5466 words)

 Computational Global Optimization in Nonlinear Systems - Lionheart Publishing "Computational Global Optimization in Nonlinear Systems," by János Pintér, presents a concise, practical introduction to models and algorithms that enable the analysis and solution of nonlinear decision problems in the presence of multiple optima. The LGO integrated modeling and solver system is introduced and used to solve these examples. Pintér's research interests include nonlinear optimization, integrated decision support systems development and a broad range of applications. www.lionhrtpub.com /books/globaloptimization.html   (473 words)

 Nonlinear Systems   (Site not responding. Last check: 2007-11-05) Presents a well-organized collection of papers that create a snapshot of the current state of important areas such as differential geometry and integrability, symplectic geometry, nonlinear hyperbolic systems, optical solitons, and low-dimensional chaos Nonlinear Systems covers a wide range of topics in nonlinear science, from general nonlinear dynamics, soliton systems, and the solution of nonlinear differential and difference equations to the integrability of discrete nonlinear systems, and classical and quantum chaos. Its chapters reflect the current status of important nonlinear theories in various areas of applied mathematics and mathematical physics and collectively provide a comprehensive picture of new areas and their applications. www.ramex.com /title.asp?id=9232   (309 words)

 Nonlinear Dynamics and Topological Time Series Analysis Archive Nonlinear dynamics resource letter from the September 1997 Issue of the American Journal of Physics. A lot can be learned about the dynamics of two-degree of freedom Hamiltonian systems by studying SAM --a Swinging Atwood's Machine (circa 1982). A talk outlining thoughts on the future of nonlinear dynamics (circa 1995). www.drchaos.net /drchaos/intro.html   (468 words)

 CDC2000 Nonlinear Time Delay Systems   (Site not responding. Last check: 2007-11-05) It is assumed that the state-space data and the time delays are dependent on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. By letting input nonlinearity in the sector bounds as a new diagonal structured uncertainty, we transform the control problems with input nonlinearity into the robust control problems of linear systems with only structured uncertainty. In addition to LMIs for the fixed input nonlinearity, we also propose an iterative LMI optimization algorithm to find robust input sector bounds such that the given uncertain system is stable for any input nonlinearity in these sector bounds. www.mm.anadolu.edu.tr /ieeecss/39cdc/CD00S17F.HTM   (931 words)

 Complex Systems Home Page   (Site not responding. Last check: 2007-11-05) Complex (Adaptive) Systems page, which is perhaps the best overall collection of pointers to complex adaptive systems related WWW pages, but the NetQ is an interactive question and answer system created by Stewart Wilson of the Rowland Institute for authors and readers interested in complex adaptive systems. Stephanie Forrest at the University of New Mexico and is conducting research on artificial immune systems. www.cea.uba.ar /aschu/links.html   (2599 words)

 Boulder Nonlinear Systems May, 2004 — Boulder Nonlinear Systems Enters OEM Arena. Boulder Nonlinear Systems, leaders in liquid crystal optical devices, today announced the availability of its 256 X 256 analog liquid crystal spatial light modulator (SLM), which offers true grayscale response with eight bits per pixel. The 256 X 256 SLM is designed to provide superior performance in applications ranging from optical correlation and beam steering, to medical research, optical storage and telecommunications. www.bnonlinear.com /news   (167 words)

 Complex Systems and Nonlinear Dynamics Links (Long List)   (Site not responding. Last check: 2007-11-05) Echo is an ecological simulation system by Terry Jones and John Holland Tierra is a system for studying ecological and evolutionary dynamics by Tom Ray UNH Nonlinear dynamics at the University of New Hampshire www.cna.org /isaac/Complex.htm   (1327 words)

 Center for Complex Systems Research   (Site not responding. Last check: 2007-11-05) The Center for Complex Systems Research (CCSR) studies systems that display adaptive, self-organizing behavior and systems that are usually characterized by a large throughput, such as turbulent flow, lightning, and the flow of information through the internet. To describe these complex systems, we develop models and techniques drawn from nonlinear dynamics and chaos, neural nets, cellular automata, artificial life, and genetic algorithms. Each year CCSR organizes and hosts the conference Understanding Complex Systems. www.ccsr.uiuc.edu   (159 words)

 Nonlinear links London: Centre for Nonlinear Dynamics and Its Applications, University College. Complex (Adaptive) Systems Information extensive list of links related to complex systems, non-linear dynamics and neural networks. Complex Systems Another extensive list of links related to complex systems. www.nbi.dk /CATS/institutions.html   (279 words)

 NOLCOS 2004 - Nonlinear Control Systems All accepted papers that are presented at the NOLCOS symposium will appear firstly in a preprint volume distributed at the conference and secondly in a proceedings book published by Elsevier Science after the conference. Selected papers will be considered for special issues of the International Journal of Robust and Nonlinear Control and Control Engineering Practice that will appear after the conference. Based on the outcome of the reviewing process, selected contributed papers will be given the opportunity to be presented in talks of extended length as semi-plenaries. www.nolcos2004.uni-stuttgart.de   (312 words)

 LANOS Home Page To teach the methods and applications of linear and To develop nonlinear circuits and systems, and related algorithms, for engineering applications To use the rich nonlinear dynamics to improve current methods in signal processing, communications and control lanoswww.epfl.ch   (75 words)

 Nonlinear Phenomena in Complex Systems: An Interdisciplinary Journal Nonlinear Phenomena in Complex Systems: An Interdisciplinary Journal Nonlinear Phenomena in Complex Systems is a quarterly journal, which will publish original research papers. In addition there will be editorials, invited reviews, a letter section and a news section containing information on future events and book reviews www.ac.by /publications/npcs   (534 words)

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