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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 metadata14.15J Networks (MIT) 14.15J Networks (MIT)

Description

Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form a Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form aSubjects

networks | networks | crowds | crowds | markets | markets | highly connected world | highly connected world | social networks | social networks | economic networks | economic networks | power networks | power networks | communication networks | communication networks | game theory | game theory | graph theory | graph theory | branching processes | branching processes | random graph models | random graph models | rich get richer phenomena | rich get richer phenomena | power laws | power laws | small worlds | small worlds | Erd?s-Renyi graphs | Erd?s-Renyi graphs | degree distributions | degree distributions | phase transitions | phase transitions | connectedness | connectedness | and giant component | and giant component | link analysis | link analysis | web search | web search | navigation | navigation | decentralized search | decentralized search | preferential attachment | preferential attachment | epidemics | epidemics | diffusion through networks | diffusion through networks | SIR | SIR | (susceptible | (susceptible | infected | infected | removed) | removed) | SIS | SIS | susceptible) | susceptible) | strategies | strategies | payoffs | payoffs | normal forms | normal forms | Nash equilibrium | Nash equilibrium | traffic networks | traffic networks | negative externalities | negative externalities | Braess' paradox | Braess' paradox | potential games | potential games | myopic behavior | myopic behavior | fictitious play | fictitious play | repeated games | repeated games | prisoner's dilemma | prisoner's dilemma | cooperation | cooperation | perfect information | perfect information | imperfect information | imperfect information | positive externalities | positive externalities | strategic complements | strategic complements | path dependence | path dependence | diffusion of innovation | diffusion of innovation | contagion pheonomena | contagion pheonomena | Bayes's rule | Bayes's rule | Bayesian Nash equilibrium | Bayesian Nash equilibrium | first price auctions | first price auctions | second price auctions | second price auctions | social learning | social learning | Bayesian learning | Bayesian learning | copying | copying | herding | herding | herd behavior | herd behavior | informational cascades | informational cascades | decisions | decisions | social choice | social choice | Condorcet jury theorem | Condorcet jury theorem | political economy | political economyLicense

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 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 metadataDescription

Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form aSubjects

networks | crowds | markets | highly connected world | social networks | economic networks | power networks | communication networks | game theory | graph theory | branching processes | random graph models | rich get richer phenomena | power laws | small worlds | Erd?s-Renyi graphs | degree distributions | phase transitions | connectedness | and giant component | link analysis | web search | navigation | decentralized search | preferential attachment | epidemics | diffusion through networks | SIR | (susceptible | infected | removed) | SIS | susceptible) | strategies | payoffs | normal forms | Nash equilibrium | traffic networks | negative externalities | Braess' paradox | potential games | myopic behavior | fictitious play | repeated games | prisoner's dilemma | cooperation | perfect information | imperfect information | positive externalities | strategic complements | path dependence | diffusion of innovation | contagion pheonomena | Bayes's rule | Bayesian Nash equilibrium | first price auctions | second price auctions | social learning | Bayesian learning | copying | herding | herd behavior | informational cascades | decisions | social choice | Condorcet jury theorem | political economyLicense

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 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

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

See all metadata