Journal
Between February 15 and 18, I visited Prof. Zhigang Zheng at Huaqiao University in Xiamen, for discussions and I gave a seminar talk to his group about Collective Dynamics of Coupled Oscillators. Thank you Prof. Zheng for the interesting discussions and the great hospitality in beautiful Xiamen! 😄
Bohuan Lin successfully defended his PhD thesis, titled Interplay between dynamics and geometry in integrable systems and engineering problems, on January 31. Bohuan was co-supervised by Holger Waalkens and me. I could only attend the defense online, but I had the opportunity to meet Bohuan in person one week later in Suzhou. Congratulations Dr. Lin, and best wishes for the future! 😄
The 2022 Suzhou Area Young Mathematicians Workshop took place on November 26-27. This was the third workshop in this series and it was hosted by XJTLU, the previous two workshops having been hosted by DKU and Soochow University. At the workshop, I gave a presentation about the recently published work on externally forced Winfree oscillators.
A paper with Bohuan Lin and Holger Waalkens on toric foliations has been published in Regular and Chaotic Dynamics. From the paper:
In 2005 Dullin et al. proved that the non zero vector of Maslov indices is an eigenvector with eigenvalue 1 of the monodromy matrices of an integrable Hamiltonian system. We take a close look at the geometry behind this result and extend it to the more general context of possibly non-Hamiltonian systems. We construct a bundle morphism defined on the lattice bundle of an (general) integrable system, which can be seen as a generalization of the vector of Maslov indices. The nontriviality of this bundle morphism implies the existence of common eigenvectors with eigenvalue 1 of the monodromy matrices, and gives rise to a corank 1 toric foliation refining the original one induced by the integrable system. Furthermore, we show that, in the case where the system has 2 degrees of freedom, this implies the existence of a compatible free
action on the regular part of the system.
The last paper with Jian Gao on the collective dynamics of second-order oscillators has been accepted for publication in Chaos. From the paper:
The synchronization process in oscillator networks, such as in the Kuramoto model, is typically driven by the formation of a large synchronized cluster that gradually absorbs more oscillators. This process can be disrupted by the formation of smaller synchronized clusters that compete with the main one. Such smaller clusters lead to non-stationary states where the order parameter varies periodically in time in contrast to coherent stationary states where it is constant. In this paper, we consider oscillators with inertia and we study the formation of smaller synchronized clusters. We find that inertia plays a crucial role in the formation of such clusters and the increase of inertia leads to a strengthening of the secondary clusters at the expense of the main cluster. We use numerical experiments, a theoretical analysis of the mean-field equations, and a simplified model to explain different aspects of the formation of secondary synchronized clusters and non-stationary states.
A paper with Georg Wilding, Keimpe Nevenzeel, Rien van de Weygaert, Gert Vegter, Pratyush Pranav, Bernard Jones, and Job Feldbrugge on the persistent homology of the large scale structures in ΛCDM cosmological models has been accepted for publication in the Monthly Notices of the Royal Astronomical Society. More details and the paper can be found here.
Jian Gao, my third PhD student, successfully defended today his PhD thesis on the Synchronization of coupled second-order Kuramoto oscillators. Congratulations Dr. Gao 😄!
Yongjiao Zhang, my second PhD student, successfully defended last Monday her thesis on externally forced Winfree systems at the University of Groningen. Congratulations Dr. Zhang!
The opening conference of the Zu Chongzhi Research Center for Mathematics and Computational Sciences takes place October 31 to November 3, 2019 at Duke Kunshan University. I am giving a talk with title On the topology of integrable Hamiltonian fibrations.
Starting October 1st, 2019 I will be appointed Associate Professor of Mathematics at the Zu Chongzhi Center for Mathematics and Computational Sciences of Duke Kunshan University in Kunshan, China.