14369

1332 دكتري

دكتري

رياضي كاربردي

اصفهان : دانشگاه صنعتي اصفهان

1397

[هفده]، [۱۳۵]ص.: مصور، نمودار

رضا مزروعي سبداني

رضا خوش سير قاضياني

حسين خيري، مجيد گازر

1397/12/04

كتابنامه

رياضي

رياضي

1397/12/04

ID1332 دكتري

Numerical normal form of symmetric bifurcations of maps Zohreh Eskandari Shahraki zohre eskandari@math iut ac ir January 16 2019 Doctor of Philosophy Thesis Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Reza Mazrooei Sabadani mazrooei@cc iut ac ir Advisor Dr Reza Khoshsiar Ghaziani khoshsiar@sci sku ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Department of Applied Mathematics and Computer Science Shahrekord University Shahrekord88186 34141 Iran Abstract There has been much more progress in numerical approaches for generic dynamical sys tems This has culminated in the packages Auto07 and matcont There is a special versionmatcontm that is devoted to maps This toolbox supports numerical continuation and bi furcation analysis of xed points and cycles of iterated maps matcontm detects limit point period doubling and Neimark Sacker points and supports continuation of these bifurcationsin two control parameters Along such bifurcation curves all codimension 2 bifurcations arealso detected The critical normal form coe cients of codim 1 and codim 2 bifurcations arecomputed as developed In the presence of symmetries certain generic conditions in the analysis are no longer satis ed Therefore we studied how to adapt matcontm in the case of symmetries Key Words Bifurcation critical normal form coe cients map normal form numericalnormal form numerical continuation symmetric bifurcation MSC 2010 37C85 37Cxx 37M20 37N40 37N99 1 IntroductionSymmetric bifurcation theory has a rich history with many beautiful theoretical results seee g 8 9 and also see in particular for maps 3 In many case studies the form of themodel allows an analytical exploration of the e ect of symmetry Meanwhile the developmentof numerical tools to study bifurcations with symmetry is limited There has been much more progress in numerical approaches for generic dynamical sys tems This has culminated in the packages auto07p 2 and matcont 5 There is a specialversion matcontm 11 that is devoted to maps This toolbox supports numerical continua tion and bifurcation analysis of xed points and cycles of iterated maps matcontm detectslimit point period doubling and Neimark Sacker points and supports continuation of these

رضا مزروعي سبداني

رضا خوش سير قاضياني

حسين خيري، مجيد گازر