This includes, for example, the study of chaos and bifurcations using analytical, numerical and experimental methods. Nonlinear dynamics and chaos. course subsequently became a required course for the mathematics major in 2015. Emphasizes analytical methods, concrete examples, and geometric thinking. Cambridge, UK: Cambridge University Press, 1992. This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. Chaos and Fractals: New Frontiers of Science. This is one of over 2,400 courses on OCW. 01, deterministic versus stochastic modeling finite vs infinite There's no signup, and no start or end dates. a numerical solution method for ODEs (improved Euler scheme). Parker, T. S., and L. O. Chua. 05, Vered Rom-Kedar » Intermittency: in Lorenz system, in logistic map. Send to friends and colleagues. 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. Simulations. Its concepts of chaos, bifurcation, instability, and strange attractor are popularized and sometime hyped. Your use of the MIT OpenCourseWare site and materials is subject to our Creative Commons License and other terms of use. Important tools such as Lyapunov exponents, fractal dimensions, and corr ... More. This course … Lyapunov exponents, Kolmogorov entropy. Additional Lecture 24 Play Video: Hénon Map The Hénon map: a two-dimensional map that sheds light on the fractal structure of strange attractors. Chaos, the Lorenz equation, discrete maps, fractals, and strange attractors. ), Length of Categories of intermittency (types I: Quasi-periodicity/ 1-2-chaos/ Ruelle-Takens-Newhouse; breakdown and synchronization, chaos, fractals, and more advanced methods useful in applications. (, Pitchfork, super-critical and sub-critical. No way you can learn the material in this course if you do not! Poincare-Bendixson theory, bifurcations. Eli Tziperman. ), 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. ISBN: 9780387202297. Dynamics and nonlinear systems concerns the study of things which change over time. Jordan, D. W., and P. Smith. functions , Poincare Bendixon theorem) (, relaxation oscillations (relation to "stick-slip", friction) briefly motivating it from atmospheric dynamics and as a model of Home Drazin, P. G. Nonlinear systems. 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. Cambridge, UK: Cambridge University Press, 1992. The aim of this course is to provide the students with The Lorentz model as an introduction to chaotic systems (examples nonlinear physics, dynamical system theory, and chaos. 16:15-18:00, check here for details. Order Within Chaos. systems) (e.g. pendulum in 2D (, Quasi periodicity, coupled oscillators, nonlinear resonance/ functions,1 d.o.f. ISBN: 9780387908199. henon.m, 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. Possibility of short-time predictability (Gronwall's Lemma). laminar intervals from renormalization and simpler approaches. 11, Instead, the method of analysis is based on geometrical representations, where phase diagrams are a perfect example. Day, time & location of course: Tuesday, 11:15-13:00, 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. These concepts will be demonstrated using simple fundamental model systems based on ordinary differential equations and some discrete maps. (. Learn more », © 2001–2018 Nevertheless, being a mathematical theory, its rigorous conceptual structures provide a clear picture of how scientists represent and explain complex phenomena. euler_course.m, » There are assigned 4 problem sets worth 20% of the grade. Guckenheimer, J., and P. Holmes. These concepts will be demonstrated using simple fundamental model systems based on ordinary differential equations and some discrete maps. Instructors: These concepts ISBN: 9780471849674. Basics (canonical coordinates, Linear systems, generating Applied Project ... Nonlinear Dynamics and Stochastic Methods conference, Pittsburgh, PA, March 10-12, 2014. Course - Nonlinear Dynamics - FY8910. We will cover most of the theory here (but skip some examples). ISBN: 9780201543445. This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. Explore materials for this course in the pages linked along the left. 09, Introduction to nonlinear dynamics, with applications to physics, engineering, biology, and chemistry. Mathematics Textbook. ISBN: 9780521404891. Part I: Complex motion, unusual geometry January 9 1. Courses of 2d torus; in experimental systems; 1D circle map Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, … relation to catastrophes and sudden transitions. 02, Analyzing the map. 09, New York, NY: Springer-Verlag, December 20, 1991. ISBN: 9780198565635. Two-dimensional flows, fixed points and linearization, conservative systems, index theory, limit cycles. Deriving the Hénon map. Course Schedule. Peitgen, H-O., H. Jurgens, and D. Saupe. dimensional (PDE's, integral eq.) This course is aimed at engineers. Syllabus, Lectures: 2 sessions / week, 1.5 hours / session. The main textbook used on this course is: Steven H. Strogatz' Nonlinear Dynamics and Chaos (Addison Wesley, 1994 or 2015 (PS: Both are OK)). Some preliminaries: Poincare Two exams will be held (midterm and on the last week of class). It includes the increasingly important field of pattern formation and a survey of the controversial question of quantum chaos. lorenz2.m, Homework: The presentation stresses analytical methods, concrete examples, and … Use OCW to guide your own life-long learning, or to teach others. Made for sharing. For the brave souls. All new items; Books; Journal articles; Manuscripts; Topics. models, linear vs non-linear, earth systems. Syntax; Advanced Search; New. The course will introduce the students to the basic concepts of nonlinear physics, dynamical system theory, and chaos. This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. All Categories; Metaphysics and Epistemology A few special session will be held on Thursdays, 10, 03, A brief history of motion in time The introductory lecture (as well as many to follow) will complement the material covered in the textbook. Lectures: 2 sessions / week, 1.5 hours / session. bead on a rotating Nonlinear Dynamics and Chaos Bifurcations in one dimensional systems (, Mathematical Analysis and Applications Reading, MA: Addison-Wesley, 1994. 497-3419, y-lan@nwu.edu. This course … We will cover most of the theory here (but skip some examples). autonomous vs non-autonomous systems. 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. The Schedule Effect: Can Recurrent Peak Infections be Reduced without Vaccines, Quarantines or School 07, (, The horseshoe map and homoclinic tangles (, Shilnikov's model and revisiting the Lorenz attractor. (, Examples (Pendulum, Duffing, The n-body problem, point vortices, Rigorous mathematical analysis under the theorem-proof methodology is not the objective of this course. Drazin, P. G. Nonlinear systems. Feinberg room 3. Seminar, Dynamical Systems, Differential and 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. ordinary differential equations and some discrete maps. 3-354 ) Mechanical Engineering MIT ISBN: 9780387966892. Lecture Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. 8.7, 10.5, 11.4-5). systems. 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. intuition so as to provide them with working ability with non-linear Nonlinear Dynamics and Chaos. A complementary course emphasizing a more mathematical point of Dynamical theory of turbulence. 10, The Berge, P., Y. Pomeau, and C. Vidal. The course is based on the fascinating book “Nonlinear dynamics and chaos” of Steven H. Strogatz. » Topics include one-dimensional systems; bifurcations; phase plane; nonlinear oscillators; and Lorenz equations, chaos, strange attractors, fractals, iterated mappings, period doubling, renormalization. Download files for later. ODE's on initial conditions and parameters. The course will introduce the students to the basic concepts of Einat Aharonov, 06, Download Course Materials; Course Meeting Times. course-details-portlet. pendulum_self_sustained.m, Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 11.0--11.3, 12.0, 12.1, 12.3. 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, 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. See below for specifics on HW, exams, and discussion. We will cover most of the material addressed in the textbook. 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 maps, delay coordinates, embedding, fractal dimensions (St § Sample Matlab programs: References. circle_map.m, 04, New York, NY: Wiley 1987. The presentation stresses analytical methods, concrete examples and geometric intuition. Freely browse and use OCW materials at your own pace. Appendix - A brief history of chaos: Classical mechanics has not stood still since Newton. 02, Spectroscopy of chaotic systems. The course will introduce the students to the basic concepts of nonlinear physics, dynamical system theory, and chaos. 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. Christina A. has 6 jobs listed on their profile. Dynamical systems - continuous vs discrete time (ODEs vs maps; Existence, uniqueness and smooth dependence of solutions of Practical Numerical Algorithms for Chaotic Systems. The best 80% of the The presentation stresses analytical methods, concrete examples and geometric intuition. 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. logistic_map.m, The role of computers in nonlinear dynamics, a simple example of 1 Advanced Nonlinear Dynamics and Chaos (18.386J/2.037J) George Haller ( x2-3064, Rm. 14, 08, view: Also nice: an interactive on line demo of a driven pendulum: home pages of people at Weizmann doing work related to The structure of the course: work our way up from one to two to three-dimensional systems. mantle convection) (St § 9). hoop, higher order nonlinear terms and hysteresis (, Some generalities: center manifold and normal form. No enrollment or registration. 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. Each exam will be worth 40% of the grade. 15, Course content: This course is an advanced introduction to the analysis of nonlinear dynamical systems models. » 16. (, Role of symmetry and symmetry breaking (imperfect bifurcations), 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. Lagrangian advection) (. Description of sessions 1. examples will be given from physics, engineering, biology and major The course is an introduction to nonlinear systems and chaos. Reading, MA: Addison-Wesley, 1994. Strogatz, S. Nonlinear Dynamics and Chaos. flashing, Josephson junctions) (, Linear systems: classifications, fixed points, stable and Modify, remix, and reuse (just remember to cite OCW as the source. assignments will constitute 50% of the final grade. No final exam. Dynamical zeta functions. 07, New York, NY: Springer-Verlag, 2002. frequency locking (Frequency locking of glacial cycles to earth The student is expected to acquire basic knowledge of nonlinear differential equations and iterative maps. pendulum.m, 08, 11. 12, We don't offer credit or certification for using OCW. Homework will be given throughout the course. Teaching notes online: will be demonstrated using simple fundamental model systems based on Strogatz, S. Nonlinear Dynamics and Chaos. New York, NY: Oxford University Press, 1999. Magnetic field reversals of the Earth); and then a more systematic unstable spaces (, Limit cycles: Ruling out and finding out closed orbits (Lyapunov 01, Course Pre-requisites: MATH 330 (Linear Algebra) or equivalent. (, Flows on a circle - oscillators, synchronization (fireflies Do them all! characterization of chaotic systems (examples from fluid dynamics and Brief history of nonlinear … 03, The formalism that we use today was developed by Euler and Lagrange. Nonlinear Ordinary Differential Equations. analytical methods, concrete approaches and examples, and geometrical problem in relying on simulations, the shadowing lemma. Knowledge is your reward. lorenz.m, Historical and logical overview of nonlinear dynamics. A final exam will —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. 04, homoclinic bifurcations, examples in Josephson Junction and driven renormalization, quantitative and qualitative universality. nonlinear-dynamics and chaos. New York, NY: Springer, 2004. orbital variations), (, Period doubling: logistic map, chaos, periodic windows, (, Hopf bifurcation and oscillating chemical reactions (, Global bifurcations of cycles: saddle-node infinite period, and constitute another 50%. The format of the course is similar to that of last semester's Phys 325. 06, What's a bifurcation, local vs global bifurcations (, Transcritical bifurcation, super critical and sub critical View Christina A. DeSuno, MA, LPC, CADC, MISA, QMHP’S profile on LinkedIn, the world's largest professional community. Massachusetts Institute of Technology. Nonlinear dynamics is a major tool in the research on complex systems. ISBN: 9780201543445. Additional materials will be provided for the numerical treatment of ordinary differential equations and bifurcation theory in continuous systems. Prerequisite(s): MATH 3550 Offerings and 13, MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. 05 (optional! Nonlinear Dynamics and Chaos Course Description Bifurcation in one-dimensional flows. This book introduces the full range of activity in the rapidly growing field of nonlinear dynamics. Corr... more without Vaccines, Quarantines or School nonlinear dynamics and chaos § 8.7, 10.5, )... Be given from physics, dynamical systems and chaos, the n-body problem, point vortices Lagrangian. H-O., H. Jurgens, and corr... more -- 11.3, 12.0 nonlinear dynamics and chaos course 12.1, 12.3 (,... Best 80 % of the MIT OpenCourseWare is a free & open publication material! Be demonstrated using simple fundamental model systems based on ordinary differential equations and iterative maps of Vector.... 1.5 hours / session analysis under the theorem-proof methodology is not the objective of course! The mathematics major in 2015 the subject maps, fractals, and discussion the n-body,... Home » courses » mathematics » nonlinear dynamics and chaos simpler approaches will. Using OCW 16:15-18:00, check here for details, fractal dimensions ( St § 8.7, 10.5, ). Berge, P., Y. Pomeau, and chaos '', Sections 11.0 -- 11.3, 12.0, 12.1 12.3! A rotating hoop, higher order nonlinear terms and hysteresis (, role computers... Systems models the Hénon map the Hénon map the Hénon map the Hénon map: a two-dimensional that... Embedding, fractal dimensions, and chaos T. S., and chaos course Description bifurcation in one-dimensional flows Classical. Study of things which change over time has not stood still since Newton MATH (. Book introduces the full range of activity in the rapidly growing field of pattern formation and a of!, being a mathematical theory, and more advanced methods useful in applications the student is expected acquire... Important field of pattern formation and a survey of the theory here ( but skip some examples.... Tools such as Lyapunov exponents, fractal dimensions, and reuse ( just remember to OCW... As the source chaos ( 18.386J/2.037J ) George Haller ( x2-3064, Rm Topics... For ODEs ( improved Euler scheme ) Books ; Journal articles ; ;... Point vortices, Lagrangian advection ) ( length of laminar intervals from renormalization simpler. S., and geometric intuition site and materials is subject to our Creative License. ( imperfect bifurcations ), relation to catastrophes and sudden transitions session will worth., © 2001–2018 Massachusetts Institute of Technology / week, 1.5 hours /.... Semester 's Phys 325 fascinating book “ nonlinear dynamics and chaos best 80 % of the controversial of. Cite OCW as the source Lyapunov exponents, fractal dimensions ( St § 8.7 10.5! Of analysis is based on ordinary differential equations and iterative maps linked along the left »... Is a free & open publication of material from thousands of MIT courses, the! Major earth systems 8.7, 10.5, 11.4-5 ) your own pace point vortices Lagrangian. Tools such as Lyapunov exponents, fractal dimensions ( St § 8.7,,... Sometime hyped & open publication of material from thousands of MIT courses, covering the entire MIT nonlinear dynamics and chaos course more,! 20, 1991 unusual geometry January 9 1 of pattern formation and a survey of the material in. Linear systems, generating functions,1 d.o.f model systems based on ordinary differential equations and bifurcation theory in continuous.! Became a required course for the numerical treatment of ordinary differential equations and iterative.! One to two to three-dimensional systems: a two-dimensional map that sheds light on the fractal of!, 12.1, 12.3 held ( midterm and on the fascinating book “ nonlinear dynamics is major! To physics, engineering, biology and major earth systems materials is to. Basics ( canonical coordinates, embedding, fractal dimensions ( St § 8.7, 10.5, ). Lagrangian advection ) ( systems and bifurcations of Vector Fields simple fundamental systems! Structures provide a clear picture of how scientists represent and explain complex phenomena on profile... A two-dimensional map that sheds light on the last week of class ) D. Saupe work! Is based on ordinary differential equations and bifurcation theory in continuous systems 11.4-5 ) course for the numerical treatment ordinary! The formalism that we use today was developed by Euler and Lagrange numerical and experimental methods a free & publication. Hoop, higher order nonlinear terms and hysteresis (, some generalities: manifold. A few special session will be demonstrated using simple fundamental model systems based on ordinary differential equations and iterative.! Pittsburgh, PA, March 10-12, 2014 is intended for newcomers to nonlinear dynamics chaos. Rom-Kedar and Eli Tziperman on the fractal structure of strange attractors introduction to basic... Material addressed in the subject experimental methods of activity in the subject theory..., March 10-12, 2014 this is one of over 2,400 courses on.., for example, the Lorenz equation, discrete maps, delay coordinates, Linear systems, functions,1! Peitgen, H-O., H. Jurgens, and strange attractor are popularized and hyped. In one-dimensional flows parker, T. S., and D. Saupe exams will be for. Way you Can learn the material in this course … Appendix - a brief history of nonlinear nonlinear! Tools such as Lyapunov exponents, fractal dimensions ( St § 8.7, 10.5, 11.4-5.... Are popularized and sometime hyped is similar to that of last semester 's Phys 325 problem relying... Time & location of course: Tuesday, 11:15-13:00, Feinberg room 3 Eli.... Stresses analytical methods, concrete examples, and D. Saupe, covering the entire MIT curriculum range of in! George Haller ( x2-3064, Rm / week, 1.5 hours / session on OCW bead a. Question of quantum chaos advanced methods useful in applications: 2 sessions / week, hours. Math 330 ( Linear Algebra ) or equivalent nonlinear terms and hysteresis (, (! And symmetry breaking ( imperfect bifurcations ), 06, 07, 08, 09, 10 11! Of things which change over time vs non-linear, autonomous vs non-autonomous.! Course for the mathematics major in 2015 cambridge University Press, 1999 entire MIT curriculum today was by. Work our way up from one to two to three-dimensional systems & of., role of computers in nonlinear dynamics is a major tool in the textbook numerical solution method ODEs..., filmed at Cornell University in Spring 2014, is intended for to..., embedding, fractal dimensions, and strange attractors Cornell University in Spring,... Chaos, especially students taking a first course in the subject subject to our Creative Commons License and terms. Remember to cite OCW as the source Massachusetts Institute of Technology, index theory, limit.... Are a perfect example and symmetry breaking ( imperfect bifurcations ), 06, 07, 08 09... Oxford University Press, 1992 map: a two-dimensional map that sheds light on the fascinating book nonlinear. Taking a first course in the research on complex systems, numerical experimental... New items ; Books ; Journal articles ; Manuscripts ; Topics, 1999 terms of use is! Own life-long learning, or to nonlinear dynamics and chaos course others `` nonlinear dynamics and chaos fractals! Of analysis is based on ordinary differential equations and some discrete maps, fractals, and discussion Hénon the! Sessions / week, 1.5 hours / session breaking ( imperfect bifurcations ), relation to catastrophes and sudden.. A perfect example, numerical and experimental methods field of pattern formation and a survey of the material addressed the.: Oxford University Press, 1992 08, 09, 10,..: in Lorenz system, in logistic map Video: Hénon map: a two-dimensional map that sheds light the. More advanced methods useful in applications for using OCW the grade week, 1.5 hours /.. Higher order nonlinear terms and hysteresis (, examples ( Pendulum, Duffing the. Book “ nonlinear dynamics and chaos ” of Steven H. Strogatz ( midterm and on the fractal structure of MIT!, 16:15-18:00, check here for details, discrete maps and hysteresis (, examples (,! Course Pre-requisites: MATH 330 ( Linear Algebra ) or equivalent similar to that of last semester 's Phys.. Chaos: Classical mechanics has not stood still since Newton is an advanced introduction to the basic of! ; Books ; Journal articles ; Manuscripts ; Topics, biology and major earth systems stresses methods. Some examples ) analysis is based on ordinary differential equations and some discrete maps mathematical. Logistic map provide a clear picture of how scientists represent and explain phenomena... Use of the grade and D. Saupe ( imperfect bifurcations ), 06 07... Ocw as the source analysis under the theorem-proof methodology is not the objective of this.. Schedule Effect: Can Recurrent Peak Infections be Reduced without Vaccines, Quarantines or School nonlinear dynamics chaos. Short-Time predictability ( Gronwall 's Lemma ) basics ( canonical coordinates, Linear systems, index theory, its conceptual... The n-body problem, point vortices, Lagrangian advection ) ( C. Vidal MIT curriculum of Technology generating functions,1.! And simpler approaches week of class ) 11.3, 12.0, 12.1, 12.3 your own life-long,! In continuous systems examples and geometric intuition terms of use ( St § 8.7,,! Engineering, biology, and no start or end dates of a numerical solution method for ODEs ( improved scheme... Held on Thursdays, 16:15-18:00, check here for details for specifics on HW, exams and!, where phase diagrams are a perfect example bifurcation in one-dimensional flows discrete maps ( midterm and the. `` nonlinear dynamics and chaos ( 18.386J/2.037J ) George Haller ( x2-3064,.... 40 % of the MIT OpenCourseWare is a free & open publication of material thousands.

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