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18.385J Nonlinear Dynamics and Chaos (MIT) 18.385J Nonlinear Dynamics and Chaos (MIT)

Description

This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software. This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.Subjects

Phase plane | Phase plane | limit cycles | limit cycles | Poincare-Bendixson theory | Poincare-Bendixson theory | Time-dependent systems | Time-dependent systems | Floquet theory | Floquet theory | Poincare maps | Poincare maps | averaging | averaging | Stability of equilibria | Stability of equilibria | near-equilibrium dynamics | near-equilibrium dynamics | Center manifolds | Center manifolds | elementary bifurcations | elementary bifurcations | normal forms | normal forms | chaos | chaos | 18.385 | 18.385 | 2.036 | 2.036License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.385 Nonlinear Dynamics and Chaos (MIT) 18.385 Nonlinear Dynamics and Chaos (MIT)

Description

Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear coupled oscillators in biology and physics. Perturbation, averaging theory. Parametric resonances, Floquet theory. Relaxation oscillations. Hysterises. Phase locking. Chaos: Lorenz model, iterated mappings, period doubling, renormalization. Fractals. Hamiltonian systems, area preserving maps; KAM theory.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc. Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear coupled oscillators in biology and physics. Perturbation, averaging theory. Parametric resonances, Floquet theory. Relaxation oscillations. Hysterises. Phase locking. Chaos: Lorenz model, iterated mappings, period doubling, renormalization. Fractals. Hamiltonian systems, area preserving maps; KAM theory.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.Subjects

Phase plane | Phase plane | limit cycles | limit cycles | Poincare-Bendixson theory | Poincare-Bendixson theory | Time-dependent systems | Time-dependent systems | Floquet theory | Floquet theory | Poincare maps | Poincare maps | averaging | averaging | Stability of equilibria | Stability of equilibria | near-equilibrium dynamics | near-equilibrium dynamics | Center manifolds | Center manifolds | elementary bifurcations | elementary bifurcations | normal forms | normal forms | chaos | chaosLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.243J Dynamics of Nonlinear Systems (MIT) 6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems. This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.Subjects

nonlinear systems | nonlinear systems | deterministic dynamical systems | deterministic dynamical systems | ordinary differential equations | ordinary differential equations | planar autonomous systems | planar autonomous systems | Picard iteration | Picard iteration | contraction mapping theorem | contraction mapping theorem | Bellman-Gronwall lemma | Bellman-Gronwall lemma | Lyapunov methods | Lyapunov methods | feedback linearization | feedback linearization | nonlinear circuits | nonlinear circuits | control systems | control systems | local controllability | local controllability | volume evolution | volume evolution | system analysis | system analysis | singular perturbations | singular perturbations | averaging | averaging | local behavior | local behavior | trajectories | trajectories | equilibria | equilibria | storage functions | storage functions | stability analysis | stability analysis | continuity | continuity | differential equations | differential equations | system models | system models | parameters | parameters | input/output | input/output | state-space | state-space | 16.337 | 16.337License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.385 Nonlinear Dynamics and Chaos (MIT)

Description

Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear coupled oscillators in biology and physics. Perturbation, averaging theory. Parametric resonances, Floquet theory. Relaxation oscillations. Hysterises. Phase locking. Chaos: Lorenz model, iterated mappings, period doubling, renormalization. Fractals. Hamiltonian systems, area preserving maps; KAM theory.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.Subjects

Phase plane | limit cycles | Poincare-Bendixson theory | Time-dependent systems | Floquet theory | Poincare maps | averaging | Stability of equilibria | near-equilibrium dynamics | Center manifolds | elementary bifurcations | normal forms | chaosLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

https://ocw.mit.edu/rss/all/mit-allarchivedcourses.xmlAttribution

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See all metadata6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.Subjects

nonlinear systems | deterministic dynamical systems | ordinary differential equations | planar autonomous systems | Picard iteration | contraction mapping theorem | Bellman-Gronwall lemma | Lyapunov methods | feedback linearization | nonlinear circuits | control systems | local controllability | volume evolution | system analysis | singular perturbations | averaging | local behavior | trajectories | equilibria | storage functions | stability analysis | continuity | differential equations | system models | parameters | input/output | state-space | 16.337License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.385J Nonlinear Dynamics and Chaos (MIT)

Description

This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.Subjects

Phase plane | limit cycles | Poincare-Bendixson theory | Time-dependent systems | Floquet theory | Poincare maps | averaging | Stability of equilibria | near-equilibrium dynamics | Center manifolds | elementary bifurcations | normal forms | chaos | 18.385 | 2.036License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

https://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.Subjects

nonlinear systems | deterministic dynamical systems | ordinary differential equations | planar autonomous systems | Picard iteration | contraction mapping theorem | Bellman-Gronwall lemma | Lyapunov methods | feedback linearization | nonlinear circuits | control systems | local controllability | volume evolution | system analysis | singular perturbations | averaging | local behavior | trajectories | equilibria | storage functions | stability analysis | continuity | differential equations | system models | parameters | input/output | state-space | 16.337License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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