18.385
Nonlinear Dynamics and Chaos
Introduction to the theory of nonlinear dynamical systems with applications from science and engineering. Local and global existence of solutions, dependence on initial data and parameters. Elementary bifurcations, normal forms. Phase plane, limit cycles, relaxation oscillations, Poincare-Bendixson theory. Floquet theory. Poincare maps. Averaging. Near-equilibrium dynamics. Synchronization. Introduction to chaos. Universality. Strange attractors. Lorenz and Rossler systems. Hamiltonian dynamics and KAM theory. Uses MATLAB computing environment.
Fall 2014
Topics
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Readings
- Drazin, P. G. Nonlinear Systems . Cambridge University Press, 2012. ISBN: 9781139172455.
- Peitgen, H-O, H. Jurgens, and D. Saupe. Chaos and Fractals: New Frontiers of Science . Springer, 2012. ISBN: 9781468493962.
- Parker, T. S., and L. O. Chua. Practical Numerical Algorithms for Chaotic Systems . Springer, 2011. ISBN: 9781461281214.
- Jordan, D. W., and P. Smith. Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers . Oxford University Press, 2007. ISBN: 9780199208258.
- Berge, P., Y. Pomeau, and C. Vidal. Order Within Chaos . Wiley-VCH, 1987. ISBN: 9780471849674.
- McCuskey, S. W. Introduction to Celestial Mechanics . Addison-Wesley Publishing Company, Incorporation, 1963. ISBN: 9780201045703.
- Guckenheimer, J., and P. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields . Springer, 2002. ISBN: 9780387908199. Requires mathematical sophistication. Subject covered at a rigorous level, with proofs requiring knowledge beyond course pre-requisites (say, at the level of Coddington, E. A., and N. Levinson. Theory of Ordinary Differential Equation . McGraw-Hill, 1984. ISBN: 9780070992566.)
- Lichtenberg, A. J., and M. A. Lieberman. Regular and Chaotic Dynamics, Applied Mathematical Sciences . Springer, 1992. ISBN: 9780387977454.
Fall 2004
Topics
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Readings
- Strogatz, S. Nonlinear Dynamics and Chaos . Reading, MA: Addison-Wesley, 1994. ISBN: 9780201543445. We will cover most of the theory here (but skip some examples).
- Drazin, P. G. Nonlinear systems . Cambridge, UK: Cambridge University Press, 1992. ISBN: 9780521404891.
- Peitgen, H-O., H. Jurgens, and D. Saupe. Chaos and Fractals: New Frontiers of Science . New York, NY: Springer, 2004. ISBN: 9780387202297.
- Parker, T. S., and L. O. Chua. Practical Numerical Algorithms for Chaotic Systems . New York, NY: Springer-Verlag, December 20, 1991. ISBN: 9780387966892.
- Jordan, D. W., and P. Smith. Nonlinear Ordinary Differential Equations . New York, NY: Oxford University Press, 1999. ISBN: 9780198565635.
- Berge, P., Y. Pomeau, and C. Vidal. Order Within Chaos . New York, NY: Wiley 1987. ISBN: 9780471849674.
Prerequisites & course information
Same subject as 2.036[J] Prereq: 18.03 or 18.032 Acad Year 2027-2028: Not offered Acad Year 2028-2029: G (Fall) 3-0-9 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2014
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- MIT OpenCourseWare ↗Fall 2004
- MIT OCW syllabus ↗
- MIT OCW calendar ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.