|M.Sc Student||Uzan Nissan|
|Subject||Nonlinear Normal Modes in Coupled Limit Cycle Oscillators|
System with Time Delay
|Department||Department of Mechanical Engineering||Supervisor||Professor Oleg Gendelman|
|Full Thesis text|
In a large variety of oscillatory systems it is crucial to take into account that the coupling can cause time delays. It is most obvious in models that take into account finite speed of the signal propagation, retarded waves, etc. In current research we consider the periodic synchronous regimes of motion in a symmetric homogeneous system of delay-coupled essentially nonlinear phase-only self-excited oscillators. Such regimes turn out to be similar to nonlinear normal modes (NNMs), known for corresponding conservative system without delays, and can be found analytically.
Unlikely the conservative counterpart, the system possesses “oval” modes with constant phase shift between the oscillators, in addition to simple and self-evident symmetric / anti-symmetric modes.
Numerical simulation demonstrates that the “oval” modes may be attractors of the phase flow.
These attractors are a particular case of phase-locked solutions, rather ubiquitous in the system under investigation. The basins of attraction of these solutions are also investigated in order to discuss the effect of the history function.