Monday, Feb 24, room 221 in A22, 14:00
Seminar by Tomasz Burzyński on his PhD thesis
„Novel numerical methods in the analysis of multistable systems”
This PhD Thesis considers multistability — a phenomenon observed in nonlinear dynamical systems. In particular, it analyzes real-world multistable systems using a sample-based approach and numerical methods. The research results are described in four peer-reviewed articles and one article under review. The first paper presents the current state of knowledge of multistable systems analysis methods. Then, three consecutive papers are devoted to the yoke-bell-clapper system — a real-world, full-scale example of a multistable system. The last paper, that is under review, is devoted to the different types of energy harvesters, devices in which multistability is widely observed and investigated.
and by V Denysenko on:
Master Stability Function for networks of coupled non-smooth oscillators
The Master Stability Function (MSF) is a key criterion for assessing the stability of complete synchronization in networks of coupled identical oscillators. This approach relies on analyzing a low-dimensional variational equation around the synchronization manifold. While this technique is easily applicable to smooth oscillators, many processes in physics, engineering, and biology are modeled using non-smooth differential equations, for which the variational equation cannot be obtained. As a result, MSF estimation for non-smooth systems cannot be performed using methods available for smooth oscillators. To address this issue, we propose an extension of the MSF that enables its application to networks of non-smooth coupled oscillators.
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