TY - JOUR
T1 - Discontinuous dynamics with grazing points
AU - Akhmet, M. U.
AU - Kivilcim, A.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - 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.
AB - 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.
KW - Axial and non-axial grazing
KW - Bifurcation of cycles
KW - Discontinuous dynamical systems
KW - Grazing points and orbits
KW - Impact mechanisms
KW - Orbital stability
KW - Small parameter
KW - Variational system
UR - http://www.scopus.com/inward/record.url?scp=84962547503&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2016.02.026
DO - 10.1016/j.cnsns.2016.02.026
M3 - Journal article
AN - SCOPUS:84962547503
SN - 1007-5704
VL - 38
SP - 218
EP - 242
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
ER -