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18.385 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 metadata18.385J 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 metadata2.18 Biomolecular Feedback Systems (MIT) 2.18 Biomolecular Feedback Systems (MIT)

Description

This course focuses on feedback control mechanisms that living organisms implement at the molecular level to execute their functions, with emphasis on techniques to design novel systems with prescribed behaviors. Students will learn how biological functions can be understood and designed using notions from feedback control. This course focuses on feedback control mechanisms that living organisms implement at the molecular level to execute their functions, with emphasis on techniques to design novel systems with prescribed behaviors. Students will learn how biological functions can be understood and designed using notions from feedback control.Subjects

biomolecular feedback systems | biomolecular feedback systems | systems biology | systems biology | modeling | modeling | feedback | feedback | cell | cell | system | system | control | control | dynamical | dynamical | input/output | input/output | synthetic biology | synthetic biology | techniques | techniques | transcription | transcription | translation | translation | transcriptional regulation | transcriptional regulation | post-transcriptional regulation | post-transcriptional regulation | cellular subsystems | cellular subsystems | dynamic behavior | dynamic behavior | analysis | analysis | equilibrium | equilibrium | robustness | robustness | oscillatory behavior | oscillatory behavior | bifurcations | bifurcations | model reduction | model reduction | stochastic | stochastic | biochemical | biochemical | simulation | simulation | linear | linear | circuit | circuit | design | design | biological circuit design | biological circuit design | negative autoregulation | negative autoregulation | toggle switch | toggle switch | repressilator | repressilator | activator-repressor clock | activator-repressor clock | IFFL | IFFL | incoherent feedforward loop | incoherent feedforward loop | bacterial chemotaxis | bacterial chemotaxis | interconnecting components | interconnecting components | modularity | modularity | retroactivity | retroactivity | gene circuit | gene circuitLicense

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 metadata18.385J 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

chaos | chaos | Floquet theory | Floquet theory | Poincare-Bendixson theory | Poincare-Bendixson theory | phase plane | phase plane | limit cycles | limit cycles | time-dependent systems | time-dependent systems | Poincare maps | Poincare maps | stability of equilibria | stability of equilibria | near-equilibrium dynamics | near-equilibrium dynamics | center manifolds | center manifolds | elementary bifurcations | elementary bifurcations | normal forms | normal formsLicense

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

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

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

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

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

See all metadata2.18 Biomolecular Feedback Systems (MIT)

Description

This course focuses on feedback control mechanisms that living organisms implement at the molecular level to execute their functions, with emphasis on techniques to design novel systems with prescribed behaviors. Students will learn how biological functions can be understood and designed using notions from feedback control.Subjects

biomolecular feedback systems | systems biology | modeling | feedback | cell | system | control | dynamical | input/output | synthetic biology | techniques | transcription | translation | transcriptional regulation | post-transcriptional regulation | cellular subsystems | dynamic behavior | analysis | equilibrium | robustness | oscillatory behavior | bifurcations | model reduction | stochastic | biochemical | simulation | linear | circuit | design | biological circuit design | negative autoregulation | toggle switch | repressilator | activator-repressor clock | IFFL | incoherent feedforward loop | bacterial chemotaxis | interconnecting components | modularity | retroactivity | gene circuitLicense

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 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

chaos | Floquet theory | Poincare-Bendixson theory | phase plane | limit cycles | time-dependent systems | Poincare maps | stability of equilibria | near-equilibrium dynamics | center manifolds | elementary bifurcations | normal formsLicense

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 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

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See all metadata