Gebze Technical University General Seminars

Discontinuous dynamics with grazing points
Ayşegül Kıvılcım
İstanbul Aydın Üniversitesi, Turkey
Özet : Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends on near solutions is constructed. Orbital stability of grazing cycles is examined by linearization. Small parameter method is extended for analysis of neighborhoods of grazing orbits, and grazing bifurcation of cycles is observed in an example. Linearization around an equilibrium grazing point is discussed. The mathematical background of the study relies on the theory of discontinuous dynamical systems [1]. Our approach is analogous to that one of the continuous dynamics analysis and results can be extended on functional differential, partial differential equations and others. Appropriate illustrations with grazing limit cycles and bifurcations are depicted to support the theoretical results. As an example, a coupled Van der Pol oscillators with impacts is taken into account. In addition to these results, non-autonomous grazing phenomenon is investigated through periodic systems and their solutions. The analysis is different than for autonomous systems in many aspects. Conditions for the existence of a linearization have been found. Stability of a periodic solution and its persistence under regular perturbations are investigated. Through examples, the theoretical results are visualized.
  Tarih : 09.12.2016
  Saat : 14:00
  Yer : Gebze Teknik Üniversitesi, Matematik Bölümü Seminer Odası
  Dil : English
  Ek Dosya : Özet