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LCN2 Seminar: The two-community noisy Kuramoto model

22 February 2019
Gorlaeus Building
Einsteinweg 55
2333 CC Leiden
Science club

This month's LCN2 seminar

Speaker: Janusz Meylahn

Title: The two-community noisy Kuramoto model

Abstract: We study the noisy Kuramoto model for two interacting communities of oscillators, where we allow the interaction in and between communities to be positive or negative. We find that, in the thermodynamic limit where the size of the two communities tends to infinity, this model exhibits non-symmetric synchronized solutions that bifurcate from the symmetric synchronized solution corresponding to the one-community noisy Kuramoto model, even in the case where the phase difference between the communities is zero and the interaction strengths are symmetric. The solutions are given by fixed points of a dynamical system. We find a critical condition for existence of a bifurcation line, as well as a pair of equations determining the bifurcation line as a function of the interaction strengths. Using the latter we are able to classify the types of solutions that are possible and thereby identify the phase diagram of the system. We also analyze properties of the bifurcation line in the phase diagram and its derivatives, calculate the asymptotics, and analyze the synchronization level on the bifurcation line. Lastly we present some simulations illustrating the stability of the various solutions. We will then  apply these results to the suprachiasmatic nucleus (body-clock) to shed some light on the possible mechanisms behind the phenomenon of phase-splitting in hamsters. 

About the LCN2 seminar

This talk is part of a series of seminars organized within an ongoing scientific initiative called the "Leiden Complex Networks Network" (LCN2), which aims at bringing together scientists with a common interest in both theoretical models and empirical analyses of complex networks and random graphs. The LCN2 community that is being established shares the approach of using networks for describing real-world complex systems and aims at developing related analytical and numerical methods, while also being open to other research approaches for studying complex systems. The talks are designed for a broad audience, allowing for constructive exchanges of ideas between scientists from different disciplines. During and after the talk, some drinks and simple snacks are provided.

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