BIFURKASI NEIMARK-SACKER DALAM SISTEM DINAMIK DAN APLIKASINYA; ( NEIMARK-SACKER BIFURCATION IN DYNAMIC SYSTEM AND ITS APPLICATION )

Rijoly, Monalisa E, Fajar Adi Kusumo

2015 | Disertasi | FMIPA

Neimark-Sacker bifurcation is associated with the pure imaginary multiplier which is appeared on discrete dynamic system linearization near the fixed point. Closed invariant curves will be generated by that discrete dynamic system after passing bifurcation value. Near closed invariant curve, for certain parameter there exist the spiral trajectory which are either approach or avoid the curve. The spiral trajectory is called supercritical bifurcations Neimark-Sacker if they approach the closed invariant curves, while it is called subcritical bifurcations Neimark-Sacker if they avoid the closed invariant curves. In this thesis, we deal with the normal form of Neimark-Sacker, the fixed point which is generated from that normal form, and the influence of parameter to the stability of that fixed point. We also give some conditions if the normal form of the bifurcation Neimark-Sacker is generalized to generic form, the stability of closed invariant curve that occured with effection of bifurcation value, and some examples related to application of bifurcations Neimark-Sacker.

Kata Kunci : N