9347

8629

كارشناسي ارشد

علوم رياضي- رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

يازده،59ص:مصور،جدول، نمودار

ص.ع.به فارسي و انگليسي

رسول عاشقي

حميدرضا ظهوري زنگنه

17/9/93

مجيد گازر، رضا مزروعي

رياضي

ID8629

Canard Cycles In Global Dynamics Samir Ahrami s ahrami@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Asheghi r asheghi@ cc iut ac ir Advisor Dr Hamidreza Zohouri Zangeneh hamidz@cc iut ac ir 2010 MSC 37B15 34A34 37A25 94A60 39A33 37D45 Keywords Canard Slow Fast Systems Delay to Bifurcation Tritrophic Food Chain AbstractThis thesis is devoted to the study of limit cycles appearing in singularly perturbed families of planarvector elds We consider an family of vector elds on a 2 manifold that for 0 has a curveof singular points Such a curve will be called a slow curve and will be denoted S In general Sconsists of hyperbolically attracting points hyperbolically repelling points and fold points dependingon whether the linear part of the vector eld at that point of S has a negative nonzero eigenvalue apositive nonzero eigenvalue or 2 zero eigenvalues we will only consider fold points of nilpotent type The main subject that we deal with is to describe the dynamics near a so called slow fast system focusing rst on common slow fast cycles Fast orbits are regular orbits The presence of a curveof singular points typically reduces the complexity of the phase portrait points near the curve areeither attracted or repelled away from the slow curve In the neighborhood of the slow curve thebehavior of singular points is small is determined by a slow drift along the slow curve This is calledthe slow dynamics a slow fast cycle is a succession of slow parts and fast orbits such that the endpoints coincide For 0 we of course have no limit cycles limit cycles may exist for 0 small bifurcating from a slow fast cycle a common slow fast cycle is a slow fast cycle where the slow partsare either all attracting or all repelling This notion is seen in contrast with a canard cycle whichis a slow fast cycle where both attracting and repelling slow parts are present we obtain results oncanard type slow fast cycles but to present the ideas we will focus in the introduction on attractingcommon slow fast cycles the case of repelling common cycles is completely similar by inversion oftime Canard cycles are by now a well known phenomenon in the context of slow fast systems and

رسول عاشقي

حميدرضا ظهوري زنگنه

مجيد گازر، رضا مزروعي