{"id":454,"date":"2024-03-12T15:14:27","date_gmt":"2024-03-12T18:14:27","guid":{"rendered":"https:\/\/cemeai.icmc.usp.br\/tiago\/?page_id=454"},"modified":"2024-03-12T16:27:20","modified_gmt":"2024-03-12T19:27:20","slug":"bifurcation","status":"publish","type":"page","link":"https:\/\/cemeai.icmc.usp.br\/tiago\/bifurcation\/","title":{"rendered":"Bifurcation"},"content":{"rendered":"\t\t
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Bifurcation Theory\n\n<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Tuesday & Friday : 2pm – 4pm ICMC 5-004<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tMain Text Book<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tWarming-up Exercises<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Program<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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August<\/strong><\/p>

13 – Discussion and Examples.<\/p>

16 – Persistence of Fixed Points<\/p>

20 – Proof of\u00a0 Center Stable\/Unstable Manifolds<\/p>

23 – Proof of\u00a0 Center Stable\/Unstable Manifolds<\/p>

27 – Proof of\u00a0 Center Stable\/Unstable Manifolds<\/p>

30 – No lessons<\/p>

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September<\/strong><\/p>

Homework Projects<\/p>

– Invariant Foliations<\/p>

– Smoothness of centre manifolds<\/p>

– Normal forms – Auto package<\/p>

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October<\/strong><\/p>

08 – 1d centre manifolds – baby normal forms<\/p>

11 –\u00a0 1d centre manifolds – one parameter family<\/p>

15 –\u00a0 2d centre manifolds: Hopf Bifurcation 1<\/p>

22 –\u00a0 2d centre manifolds: Hopf Bifurcation 2<\/p>

25 –\u00a0 2d centre manifolds: SNIC<\/p>

29 –\u00a0 2d centre manifolds: Homoclinic<\/p>

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November<\/strong><\/p>

05 – Homoclinic bifurcation: Shilnikov<\/p>

08 – Homoclinic bifurcation: Shilnikov<\/p>

12 – Homoclinic bifurcation: Shilnikov<\/p>

15 – Coupled Systems with Periodic Motion: Floquet Theory<\/p>

19 – Coupled Systems with Periodic Motion: Poincare Map<\/p>

22 – Coupled Systems with Periodic Motion: Phase response<\/p>

26 – Coupled Systems with Periodic Motion: Averaging Theory<\/p>

29 – Kuramoto Model<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Bifurcation Theory Tuesday & Friday : 2pm – 4pm ICMC 5-004 Main Text Book Text Book 1 Warming-up Exercises Center Manifolds Program August 13 – Discussion and Examples. 16 – Persistence of Fixed Points 20 – Proof of\u00a0 Center Stable\/Unstable Manifolds 23 – Proof of\u00a0 Center Stable\/Unstable Manifolds 27 – Proof of\u00a0 Center Stable\/Unstable Manifolds […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"class_list":["post-454","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/pages\/454","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/comments?post=454"}],"version-history":[{"count":22,"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/pages\/454\/revisions"}],"predecessor-version":[{"id":514,"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/pages\/454\/revisions\/514"}],"wp:attachment":[{"href":"https:\/\/cemeai.icmc.usp.br\/tiago\/wp-json\/wp\/v2\/media?parent=454"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}