Nonlinear Oscillators in a complex network will be analyzed both mathematically and numerically to relate the spectral properties of the system with the topology of the network. Coherence of the oscillators, such as the model of Kuromoto, will be analysed.
Making use of basic knowledge in physics and mathematics, together with computer programming, the applicant will analyze the relation of the spectral properties of the oscillators and the topology of the network. Practical applications may be conducted near the end of the project.
1. Learn to analyze simple oscillators on a regular graph
2. Extend the analysis to complex network
3. Application to real networks