Networks of Oscillators That Synchronise Themselves - Prof Steven Strogatz - The Archimedeans скачать в хорошем качестве

Networks of Oscillators That Synchronise Themselves - Prof Steven Strogatz - The Archimedeans

Prof. Steven Strogatz is one of the most cited mathematicians of all time, and a leading expert in non-linear dynamics and network theory. In addition, he is a very experienced maths communicator, his outreach work including two series of columns in the New York Times, a TED talk and multiple books for a popular audience, the most of which is a New York Times bestseller. Populations of coupled oscillators are pervasive in the natural world, from swarms of rhythmically flashing fireflies to groups of pacemaker cells in the heart. Some systems of oscillators have the amazing ability to synchronize themselves, such that all the oscillators end up firing in unison, no matter how disorganized they were at the start. In this (hopefully) entertaining Zoom talk, Prof Strogatz will discuss the simplest mathematical model of a self-synchronizing system, the so-called Kuramoto model, and discuss how it behaves on different kinds of networks. Using techniques from nonlinear dynamics, numerical linear algebra, and computational algebraic geometry, we will discuss new bounds, conjectures, and open problems about the densest networks that do not always synchronize and the sparsest ones that do. This is joint work with Alex Townsend and Mike Stillman. The talk is based on this paper: https://arxiv.org/abs/1906.10627 Some prerequisite knowledge on vectors, matrices and differential equations will be useful. -------------------------------------------------------------------------------- Subscribe:    / @thearchimedeans7041   Our website: https://archim.soc.srcf.net/ Our Facebook page:   / archimedeans   Join our mailing list: https://lists.cam.ac.uk/mailman/listi... Join our Microsoft Teams: http://forms.gle/tGHnN7XhEUVCeRgr6