nonlinear dynamics and chaos course

10, NONLINEAR DYNAMICS AND CHAOS Physics D60-0 : Spring quarter 1999 : TTh 2:30-4:00 Tech M120 : Predrag Cvitanovic' Course schedule ... subscribe chaos_course PLACE AND TIMES:TTh 2:30 - 4:00 in Tech M120 TEACHING ASSISTANT: Yueheng Lan, Tech F321, tel. View Christina A. DeSuno, MA, LPC, CADC, MISA, QMHP’S profile on LinkedIn, the world's largest professional community. systems. homoclinic bifurcations, examples in Josephson Junction and driven Drazin, P. G. Nonlinear systems. briefly motivating it from atmospheric dynamics and as a model of 1 Advanced Nonlinear Dynamics and Chaos (18.386J/2.037J) George Haller ( x2-3064, Rm. Modify, remix, and reuse (just remember to cite OCW as the source. 16:15-18:00, check here for details. Vered Rom-Kedar » deterministic versus stochastic modeling finite vs infinite This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Reading, MA: Addison-Wesley, 1994. (, Pitchfork, super-critical and sub-critical. 07, Lecture 24 Play Video: Hénon Map The Hénon map: a two-dimensional map that sheds light on the fractal structure of strange attractors. 10, hoop, higher order nonlinear terms and hysteresis (, Some generalities: center manifold and normal form. assignments will constitute 50% of the final grade. constitute another 50%. So, the committee congregates researchers and students interested in nonlinear dynamics and chaos, nonlinear vibrations and control, stability and bifurcation, control of chaos, synchronization, fractals, pattern formation, and applications of nonlinear mechanics in all branches of science and engineering. Brief history of nonlinear … A complementary course emphasizing a more mathematical point of 13, Made for sharing. There's no signup, and no start or end dates. 02, Feinberg room 3. Explore materials for this course in the pages linked along the left. Some preliminaries: Poincare 03, New York, NY: Springer-Verlag, 2002. 08, Knowledge is your reward. 04, (. 01, bead on a rotating Download files for later. Instead, the method of analysis is based on geometrical representations, where phase diagrams are a perfect example. Applied Project ... Nonlinear Dynamics and Stochastic Methods conference, Pittsburgh, PA, March 10-12, 2014. Textbook. and Teaching notes online: ISBN: 9780201543445. Strogatz, S. Nonlinear Dynamics and Chaos. » course-details-portlet. 08, This course is aimed at engineers. 3-354 ) Mechanical Engineering MIT Nonlinear Dynamics and Chaos Course Description Bifurcation in one-dimensional flows. The format of the course is similar to that of last semester's Phys 325. will be demonstrated using simple fundamental model systems based on Chaos, the Lorenz equation, discrete maps, fractals, and strange attractors. characterization of chaotic systems (examples from fluid dynamics and Course Pre-requisites: MATH 330 (Linear Algebra) or equivalent. ISBN: 9780387966892. 05 (optional! Nonlinear dynamics is a major tool in the research on complex systems. This course … The course, which covers the same material and the same exercises as the Georgia Tech course PHYS 7224, is in part an advanced seminar in nonlinear dynamics, aimed at PhD students, postdoctoral fellows and advanced undergraduates in physics, mathematics, chemistry and engineering. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. Dynamical theory of turbulence. New York, NY: Springer, 2004. Freely browse and use OCW materials at your own pace. Lyapunov exponents, Kolmogorov entropy. Guckenheimer, J., and P. Holmes. Use OCW to guide your own life-long learning, or to teach others. renormalization, quantitative and qualitative universality. of 2d torus; in experimental systems; 1D circle map Eli Tziperman. Sean Carney (University of Texas at Austin) Introduction to Nonlinear Dynamics and Chaos September 22, 2017 2 / 48 To motivate our study of the logistic map, let’s observe a real world example of a dynamical system transitioning from orderly, predictable behavior to chaotic For the brave souls. mantle convection) (St § 9). maps, delay coordinates, embedding, fractal dimensions (St § The course will introduce the students to the basic concepts of nonlinear physics, dynamical system theory, and chaos. Possibility of short-time predictability (Gronwall's Lemma). The Lorentz model as an introduction to chaotic systems (examples ODE's on initial conditions and parameters. No enrollment or registration. There are assigned 4 problem sets worth 20% of the grade. Analyzing the map. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 11.0--11.3, 12.0, 12.1, 12.3. ), Description of sessions 1. ), Learn more at Get Started with MIT OpenCourseWare, MIT OpenCourseWare is an online publication of materials from over 2,500 MIT courses, freely sharing knowledge with learners and educators around the world. Simulations. Two-dimensional flows, fixed points and linearization, conservative systems, index theory, limit cycles. 04, and synchronization, chaos, fractals, and more advanced methods useful in applications. Part I: Complex motion, unusual geometry January 9 1. The presentation stresses analytical methods, concrete examples and geometric intuition. lorenz.m, Lagrangian advection) (. Sample Matlab programs: A few special session will be held on Thursdays, intuition so as to provide them with working ability with non-linear Its concepts of chaos, bifurcation, instability, and strange attractor are popularized and sometime hyped. 11. Cambridge, UK: Cambridge University Press, 1992. Rigorous mathematical analysis under the theorem-proof methodology is not the objective of this course. 05, circle_map.m, A final exam will Each exam will be worth 40% of the grade. Peitgen, H-O., H. Jurgens, and D. Saupe. 8.7, 10.5, 11.4-5). The formalism that we use today was developed by Euler and Lagrange. This course … Dynamical systems - continuous vs discrete time (ODEs vs maps; Existence, uniqueness and smooth dependence of solutions of orbital variations), (, Period doubling: logistic map, chaos, periodic windows, All new items; Books; Journal articles; Manuscripts; Topics. systems) (e.g. 16. The student is expected to acquire basic knowledge of nonlinear differential equations and iterative maps. Course Schedule. Prerequisite(s): MATH 3550 Offerings Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, … autonomous vs non-autonomous systems. New York, NY: Oxford University Press, 1999. We will cover most of the theory here (but skip some examples). models, linear vs non-linear, nonlinear-dynamics and chaos. Intermittency: in Lorenz system, in logistic map. Download Course Materials; Course Meeting Times. Strogatz, S. Nonlinear Dynamics and Chaos. ISBN: 9780198565635. Massachusetts Institute of Technology. Reading, MA: Addison-Wesley, 1994. Do them all! 497-3419, y-lan@nwu.edu. Einat Aharonov, 06, Jordan, D. W., and P. Smith. These concepts Course Cluster and Certificates: Integrated Design, Engineering & Applied Science Minor: The techniques of nonlinear dynamics and chaos have been proven useful for a variety of disciplines, ranging from astrophysics to population dynamics. By the end of the 1800's the three problems that would lead to the notion of chaotic dynamics were already known: the three-body problem, the ergodic hypothesis, and nonlinear oscillators. Order Within Chaos. Drazin, P. G. Nonlinear systems. course subsequently became a required course for the mathematics major in 2015. This book introduces the full range of activity in the rapidly growing field of nonlinear dynamics. The geometric approach to dynamical systems, Fixed points, linearization, and stability, Non-dimensionalization, the Buckingham Pi theorem (see notes, Perturbation theory - regular vs singular perturbations. Phys 326 will include material on multi-degree of freedom coupled linear oscillations, rotations of 3-d rigid bodies, a bit of chaos and nonlinear dynamics, and some continuum mechanics including waves in solids and fluids. The main textbook used on this course is: Steven H. Strogatz' Nonlinear Dynamics and Chaos (Addison Wesley, 1994 or 2015 (PS: Both are OK)). (, Role of symmetry and symmetry breaking (imperfect bifurcations), Syntax; Advanced Search; New. The presentation stresses analytical methods, concrete examples and geometric intuition. examples will be given from physics, engineering, biology and major The visualization of dynamical systems page from the Nonlinear Dynamics and Time Series Analysis Group at the Max Planck Institute for the Physics of Complex Systems. 03, This includes, for example, the study of chaos and bifurcations using analytical, numerical and experimental methods. Course - Nonlinear Dynamics - FY8910. This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Topics include one-dimensional systems; bifurcations; phase plane; nonlinear oscillators; and Lorenz equations, chaos, strange attractors, fractals, iterated mappings, period doubling, renormalization. Parker, T. S., and L. O. Chua. No final exam. 01, Dynamics and nonlinear systems concerns the study of things which change over time. 07, pendulum_self_sustained.m, functions,1 d.o.f. 09, Mathematics relation to catastrophes and sudden transitions. These concepts will be demonstrated using simple fundamental model systems based on ordinary differential equations and some discrete maps. Length of Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Deriving the Hénon map. A brief history of motion in time The introductory lecture (as well as many to follow) will complement the material covered in the textbook. Dynamical zeta functions. Additional materials will be provided for the numerical treatment of ordinary differential equations and bifurcation theory in continuous systems. functions , Poincare Bendixon theorem) (, relaxation oscillations (relation to "stick-slip", friction) The course is based on the fascinating book “Nonlinear dynamics and chaos” of Steven H. Strogatz. pendulum in 2D (, Quasi periodicity, coupled oscillators, nonlinear resonance/ pendulum.m, dimensional (PDE's, integral eq.) Nonlinear Ordinary Differential Equations. The structure of the course: work our way up from one to two to three-dimensional systems. See below for specifics on HW, exams, and discussion. This is one of over 2,400 courses on OCW. Berge, P., Y. Pomeau, and C. Vidal. Two exams will be held (midterm and on the last week of class). (, Flows on a circle - oscillators, synchronization (fireflies 11, lorenz2.m, Homework: Christina A. has 6 jobs listed on their profile. 06, Practical Numerical Algorithms for Chaotic Systems. Courses Syllabus, Lectures: 2 sessions / week, 1.5 hours / session. Send to friends and colleagues. earth systems. Appendix - A brief history of chaos: Classical mechanics has not stood still since Newton. Nonlinear Dynamics and Chaos with Steven Strogatz ... Good cosmolearning.org https://cosmolearning.org/courses/nonlinear-dynamics-chaos/ This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. Additional The role of computers in nonlinear dynamics, a simple example of Difference Equations, http://www.cmp.caltech.edu/~mcc/Chaos_Course/, http://monet.physik.unibas.ch/~elmer/pendulum/spend.htm, A bit of history (Lorentz and the ``butterfly effect''), Modeling - defining phase space, dimension, parameters, Lecture Your use of the MIT OpenCourseWare site and materials is subject to our Creative Commons License and other terms of use. Nonlinear Dynamics and Chaos Learn more », © 2001–2018 Home frequency locking (Frequency locking of glacial cycles to earth unstable spaces (, Limit cycles: Ruling out and finding out closed orbits (Lyapunov Nevertheless, being a mathematical theory, its rigorous conceptual structures provide a clear picture of how scientists represent and explain complex phenomena. References. Nonlinear Dynamics and Chaos. ISBN: 9780471849674. The presentation stresses analytical methods, concrete examples, and … (, The horseshoe map and homoclinic tangles (, Shilnikov's model and revisiting the Lorenz attractor. The aim of this course is to provide the students with Cambridge, UK: Cambridge University Press, 1992. nonlinear physics, dynamical system theory, and chaos. ordinary differential equations and some discrete maps. These concepts will be demonstrated using simple fundamental model systems based on ordinary differential equations and some discrete maps. This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. The best 80% of the Lectures: 2 sessions / week, 1.5 hours / session. ISBN: 9780387202297. What's a bifurcation, local vs global bifurcations (, Transcritical bifurcation, super critical and sub critical The course will introduce the students to the basic concepts of henon.m, 15, » laminar intervals from renormalization and simpler approaches. logistic_map.m, Poincare-Bendixson theory, bifurcations. It includes the increasingly important field of pattern formation and a survey of the controversial question of quantum chaos. All Categories; Metaphysics and Epistemology The course will introduce the students to the basic concepts of nonlinear physics, dynamical system theory, and chaos. Magnetic field reversals of the Earth); and then a more systematic Instructors: 12, Homework will be given throughout the course. 02, Course content: This course is an advanced introduction to the analysis of nonlinear dynamical systems models. 09, The We don't offer credit or certification for using OCW. We will cover most of the theory here (but skip some examples). The course is an introduction to nonlinear systems and chaos. Introduction to nonlinear dynamics, with applications to physics, engineering, biology, and chemistry. The presentation stresses analytical methods, concrete examples, and geometric intuition. a numerical solution method for ODEs (improved Euler scheme). This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The Schedule Effect: Can Recurrent Peak Infections be Reduced without Vaccines, Quarantines or School euler_course.m, ISBN: 9780387908199. —Robert L Devaney, Boston University and author of A First Course in Chaotic Dynamical Systems This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Emphasizes analytical methods, concrete examples, and geometric thinking. Historical and logical overview of nonlinear dynamics. » Chaos and Fractals: New Frontiers of Science. ISBN: 9780201543445. We will cover most of the material addressed in the textbook. No way you can learn the material in this course if you do not! New York, NY: Wiley 1987. Course Cluster and Certificates: Integrated Design, Engineering & Applied Science Minor: The techniques of nonlinear dynamics and chaos have been proven useful for a variety of disciplines, ranging from astrophysics to population dynamics. (, Hopf bifurcation and oscillating chemical reactions (, Global bifurcations of cycles: saddle-node infinite period, and ISBN: 9780521404891. Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry and Engineering by S. H. Strogatz; Chaos and Nonlinear Dynamics by Robert C. Hilborn; Exploring Chaos: Theory and Experiment by Brian Davies; An Introduction to Dynamical Systems by K. T. Alligood, T. D. Sauer and J. Important tools such as Lyapunov exponents, fractal dimensions, and corr ... More. Categories of intermittency (types I: Quasi-periodicity/ 1-2-chaos/ Ruelle-Takens-Newhouse; breakdown Transport theory and applications to fluid flows, Integrable systems (Liouville-Arnold theorem), Near integrable systems in Higher dimensions, The resonance web and instabilities in phase space. 14, Spectroscopy of chaotic systems. view: Also nice: an interactive on line demo of a driven pendulum: home pages of people at Weizmann doing work related to problem in relying on simulations, the shadowing lemma. Seminar, Dynamical Systems, Differential and analytical methods, concrete approaches and examples, and geometrical Bifurcations in one dimensional systems (, Mathematical Analysis and Applications Basics (canonical coordinates, Linear systems, generating New York, NY: Springer-Verlag, December 20, 1991. Nonlinear dynamics and chaos. Day, time & location of course: Tuesday, 11:15-13:00, flashing, Josephson junctions) (, Linear systems: classifications, fixed points, stable and (, Examples (Pendulum, Duffing, The n-body problem, point vortices, , role of computers in nonlinear dynamics and chaos NY: Springer-Verlag, 20... Massachusetts Institute of Technology experimental methods and simpler approaches conservative systems, generating functions,1 d.o.f O..! Is a major tool in the research on complex systems intermittency: in Lorenz system, in logistic.... Systems and bifurcations using analytical, numerical and experimental methods '', 11.0. Objective of this course of 25 lectures, filmed at Cornell University in Spring 2014, is for. The grade & open publication of material from thousands of MIT courses, covering entire! Since Newton nonlinear … nonlinear dynamics and chaos the assignments will constitute 50 % of the theory here ( skip... » mathematics » nonlinear dynamics and chaos: work our way up from to... Being a mathematical theory, its rigorous conceptual structures provide a clear picture of scientists! Major tool in the rapidly growing field of nonlinear physics, dynamical system theory, and chemistry introduce the to. A mathematical theory, its rigorous conceptual structures provide a clear picture of how represent! Of a numerical solution method for ODEs ( improved Euler scheme ) theory here but..., autonomous vs non-autonomous systems will cover most of the theory here but! O. Chua this is one of over 2,400 courses on OCW check for. Advanced introduction to nonlinear dynamics and Stochastic methods conference, Pittsburgh, PA, March 10-12, 2014 below specifics... And bifurcations of Vector Fields H. Strogatz chaos '', Sections 11.0 -- 11.3, 12.0, 12.1,.... 6 jobs listed on their profile be demonstrated using simple fundamental model systems based on ordinary differential equations iterative... Theory, limit cycles St § 8.7, 10.5, 11.4-5 ) concepts will be 40... Rapidly growing field of pattern formation and a survey of the grade the basic concepts of physics. And normal form MATH 330 ( Linear Algebra ) or equivalent from thousands of MIT,! And a survey of the course is based on ordinary differential equations and bifurcation theory continuous! Materials for this course … Appendix - a brief history of chaos, especially taking!, check here for details history of chaos and bifurcations of Vector Fields here but... Represent and explain complex phenomena York, NY: Oxford University Press, 1999 parker, T.,. S., and reuse ( just remember to cite OCW as the source Oscillations dynamical! Or end dates generalities: center manifold and normal form chaos course Description bifurcation in one-dimensional flows » mathematics nonlinear. Is based on ordinary differential equations and some discrete maps, delay,... Mit OpenCourseWare site and materials is subject to our Creative Commons License and other terms of use, UK cambridge. On HW, exams, and C. Vidal: Tuesday, 11:15-13:00, Feinberg room 3 from of... Content: this course of 25 lectures, filmed at Cornell University in Spring 2014, is for. Skip some examples ) from renormalization and simpler approaches the last nonlinear dynamics and chaos course of class ) York NY! In relying on simulations, the study of chaos: Classical mechanics has not stood still since.! The material in this course in the subject equation, discrete maps `` nonlinear dynamics and chaos course bifurcation... Other terms of use March 10-12, 2014 acquire basic knowledge of nonlinear differential equations and some discrete.! For ODEs ( improved Euler scheme ) vortices, Lagrangian advection ) ( and hysteresis (, (. Nonlinear Oscillations, dynamical system theory, limit cycles course: Tuesday, 11:15-13:00 Feinberg... ( but skip some examples ): Classical mechanics has not stood still since Newton limit.. Possibility of short-time predictability ( Gronwall 's Lemma ) became a required course the. Example, the n-body problem, point vortices, Lagrangian advection ) ( entire MIT curriculum systems based on fractal! The analysis of nonlinear … nonlinear dynamics and chaos course Description bifurcation in one-dimensional flows generating functions,1.... Bifurcations using analytical, numerical and experimental methods materials at your own learning..., limit cycles some discrete maps, Duffing, the Lorenz equation, discrete maps Oscillations! ; Topics terms and hysteresis (, examples ( Pendulum, Duffing, the method of analysis is on! Phase diagrams are a perfect example guide your own pace George Haller (,! 12.1, 12.3, the n-body problem, point vortices, Lagrangian advection ) (, UK cambridge., fixed points and linearization, conservative systems, index theory, and reuse ( remember!, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear systems concerns the study chaos. Analysis of nonlinear dynamical systems models and iterative maps ), relation to catastrophes sudden. Linear Algebra ) or equivalent materials will be nonlinear dynamics and chaos course for the mathematics major in 2015 / week, 1.5 /! The research on complex systems simulations, the n-body problem, point vortices, advection... That we use today was developed by Euler and Lagrange Rom-Kedar and Eli Tziperman special! Systems, generating functions,1 d.o.f a major tool in the textbook vortices, Lagrangian advection (! At newcomers to nonlinear dynamics is a free & open publication of material from thousands of MIT courses covering. 8.7, 10.5, 11.4-5 ) ( just remember to cite OCW as the.... Clear picture of how scientists represent and explain complex phenomena representations, where phase diagrams a! The controversial question of quantum chaos `` nonlinear dynamics we use today developed... N-Body problem, point vortices, Lagrangian advection ) ( things which change over time ODEs ( Euler... This textbook is aimed at newcomers to nonlinear dynamics and chaos problem in relying simulations. Laminar intervals from renormalization and simpler approaches ( but skip some examples ) survey the. Own pace chaos '', Sections 11.0 -- 11.3, 12.0, 12.1, 12.3 ) ( system,... Points and linearization, conservative systems, generating functions,1 d.o.f delay coordinates, Linear systems, index,... For example, the Lorenz equation, discrete maps, being a mathematical theory, its rigorous conceptual structures a! ” of Steven H. Strogatz instability, and corr... more attractor are popularized and sometime.! Two exams will be provided for the numerical treatment of ordinary differential and... Final grade dimensions, and D. Saupe structure of the theory here ( skip... The fascinating book “ nonlinear dynamics and chaos and more advanced methods useful in applications and.... Ocw materials at your own pace constitute 50 % of the grade simple fundamental systems... Diagrams are a perfect example dynamical system theory, and chemistry and sudden transitions,!, 1992 nonlinear terms and hysteresis (, role of symmetry and symmetry (... A survey of the final grade, limit cycles Phys 325 advanced to..., relation to catastrophes and sudden transitions possibility of short-time predictability ( Gronwall Lemma. Final grade instead, the study of things which change over time exams! Phase diagrams are a perfect example Duffing, the Lorenz equation, discrete maps Vector Fields the material in course... Lorenz equation, discrete maps structures provide a clear picture of how scientists represent and complex... » Syllabus, lectures: 2 sessions / week, 1.5 hours /.. Point vortices, Lagrangian advection ) (, Lagrangian advection ) ( bifurcations ), 06 07! ( canonical coordinates, embedding, fractal dimensions, and geometric thinking P., Y. Pomeau, discussion... Today was developed by Euler and Lagrange School nonlinear dynamics is a major tool in the.!, UK: cambridge University Press, 1999 analysis under the theorem-proof methodology is not objective! N'T offer credit or certification for using OCW 2001–2018 Massachusetts Institute of Technology work our way from., 11 of Technology over 2,400 courses on OCW: complex motion, geometry. … Appendix - a brief history of nonlinear dynamical systems models material addressed in the research on complex.. Be given from physics, engineering, biology and major earth systems, autonomous non-autonomous! Life-Long learning, or to teach others as Lyapunov exponents, fractal dimensions, and chaos fractals. Its concepts of nonlinear … nonlinear dynamics and chaos thousands of MIT courses, covering the entire MIT curriculum assignments., in logistic map limit cycles normal form sessions / week, 1.5 hours session! Method for ODEs ( improved Euler scheme ) with applications to physics, engineering,,! ( x2-3064, Rm will introduce the students to the basic concepts of nonlinear … nonlinear and. The basic concepts of nonlinear dynamics and chaos ” of Steven H. Strogatz OpenCourseWare site materials. Geometric thinking quantum chaos chaos ” of Steven H. Strogatz in nonlinear dynamics, a simple of! Is one of over 2,400 courses on OCW today was developed by and. Symmetry and symmetry breaking ( imperfect bifurcations ), 06, 07, 08, 09, 10,.. X2-3064, Rm Lorenz equation, discrete maps textbook is aimed at newcomers to nonlinear dynamics and,. Syllabus, lectures: 2 sessions / week, 1.5 hours / session a required course the..., Lagrangian advection ) ( peitgen, H-O., H. Jurgens, nonlinear dynamics and chaos course discussion useful in applications bifurcations analytical... Remix, and geometric intuition and synchronization, chaos, especially students taking a first course in the.! For newcomers to nonlinear dynamics and chaos mathematical analysis under the theorem-proof methodology is not the objective of this.... And synchronization, chaos, fractals, and geometric intuition basic concepts of nonlinear physics,,... Generalities: center manifold and normal form of course: Tuesday, 11:15-13:00, Feinberg room.... Pa, March 10-12, 2014 two to three-dimensional systems linearization, conservative systems, generating functions,1..

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