7270

6776

كارشناسي ارشد

رياضي كاربردي

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1391

يازده، 97ص.: مصور، جدول، نمودار

ص.ع. به فارسي و انگليسي

مجيد گازر

رضا خوش سير فاضيايي

21/8/91

محمدرضا رئوفي، رضا مزروعي سبداني

1396/09/21

كتابنامه

علوم رياضي

رياضي

ID6776

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

AbstractThe interaction of a Hopf bifurcation with the codimension 2 cusp bifurcationyields a codimension three bifurcation with a rich variety of dynamic behaviourand new interesting phenamena which do not exist in the fold Hopf case Thisbifurcation is called codimension 3 cusp Hopf bifurcation that is studied on thethree dimensional center manifold The focus of this thesis is determination of thedynamical behavior when a Hopf bifurcation occurs at an equilibrium point nearthe cusp bifurcation Our analysis is based on truncated normal form The S1symmetry of the normal form system leads to further reduction to a plannar vectorfield Further transformations are used to simplify the nonlinear coefficients andreduse the number of cases under consideration The invariant sets of the twodimensional truncatednormal form has been located That includs all equilibriumpoints and period orbits Codimension 1 bifurcations such as the secondary Hopfand pitchfork bifurcation are calculated in two dimensional state space Theperiodic orbit bifurcated in the secondary Hopf bifurcation are associated with thetorus bifurcation The coalesense of three equilibria happens through pitchforkbifurcation Bifurcation varieties are presented in three parameter space 1 2 3 which are called cusp Hopf and torus varieties When equilibriums point changefrom real to complex variable Then this varieties are created Because of thetransverse intersection of bifurcation varieties with any plane 3 constant 0 the study of behaviour of bifurcation varieties is reduced to three two parameter

مجيد گازر

رضا خوش سير فاضيايي

محمدرضا رئوفي، رضا مزروعي سبداني