Many natural phenomena and industry applications can be modelled as networks of coupled oscillators, including firefly flashing, neuron firing, and power grid dynamics. A common phenomenon in networks of coupled oscillators is synchronisation. Model reduction techniques aim to understand and quantify this low-dimensional emergent macroscopic dynamics. In this talk I will present the collective coordinate approach to model reduction for networks of coupled oscillators, and compare the collective coordinate approach with the widely used Ott-Antonsen approach. I will show that the collective coordinate approach yields a more accurate approximation for the macroscopic dynamics of finite networks of coupled oscillators than the Ott-Antonsen approach, and recovers well-known results in the thermodynamic limit of infinitely many oscillators.


Then, I will use the collective coordinate approach to determine necessary conditions for collective chaos to occur in networks of coupled oscillators with multimodal natural frequency distributions, which naturally give rise to multiple synchronised clusters. Through a time-scale splitting between the fast inter-cluster dynamics and slow intra-cluster dynamics, it can be shown that at least four peaks in the natural frequency distribution are necessary for collective phase chaos to occur. In addition, in cases where the time-scale splitting is invalid, chaos can also occur if there are three peaks in the natural frequency distribution. Lastly, I will show that chaos cannot occur for bimodal natural frequency distributions


About Applied and computational maths seminars

Our seminars bring together UQ's applied and computational mathematics communities.

UQ and invited scientists deliver the presentations, which are informal and promote discussion.

We welcome suggestions for speakers and topics from staff, students and visitors, and encourage students to share their work.

Our seminars are usually held on Thursdays from 3pm to 4pm.

To suggest a topic or speaker, and for more information, contact Dr Dietmar Oelz or Dr Fred Roosta-Khoransani.

Venue

Physics Annexe (building #06)
Room: 
407