Discontinuous dynamics with grazing points


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AKHMET M. , Kivilcim A.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, cilt.38, ss.218-242, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 38
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.cnsns.2016.02.026
  • Dergi Adı: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Sayfa Sayıları: ss.218-242

Özet

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of solutions 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 grazing orbits, and bifurcation of cycles is observed in an example. Linearization around an equilibrium grazing point is discussed. The results can be extended on functional differential equations, partial differential equations and others. Appropriate illustrations are depicted to support the theoretical results. (c) 2016 Elsevier B.V. All rights reserved.