Wei Lin (林 伟)
Fudan University (复旦大学)
Abstract:In this plenary talk, I will introduce some of our recent works on time series analytics, including directional interactions detections and dynamics predictions. Based on the theory of nonlinear dynamical systems as well as machine learning techniques, we develop several data-driven and model-free frameworks for realizing detections and predictions. Through comparing our frameworks with other existing methods in the literature, we show the advantages of our frameworks when they are used to deal with the data produced numerically by dynamical oscillators and collected by real experiments as well.
Nonlocal Diffusion Equations with Free Boundaries
Wantong Li (李万同)
Lanzhou University (兰州大学)
Abstract: We introduce and study a class of free boundary models with nonlocal diffusion. We show that this nonlocal problem has a unique solution defined for all time, and then examine its long-time dynamical behavior when the growth function is of Fisher-KPP type. We prove that a spreading-vanishing dichotomy holds, though for the spreading-vanishing criteria significant differences arise from the well known local diffusion model. Finally, as applications, we consider the dynamics of a nonlocal L-V competition model and a nonlocal epidemic model with free boundaries. This talk is based on joint works with Jia-Feng Cao (LUT), Yihong Du (UNE), Fang Li (SYU), Wenjie Ni (UNE) and Meng Zhao (NWNU).
How likely can a point be in different Cantor sets
Wenxia Li (李文侠)
East China Normal University (华东师范大学)
摘 要：对于一个给定的实数$x\in (0,1)$, 我们考虑一类单参数的康托集合族$C_\lambda $, 变动该参数$\lambda $使得$x\in C_\lambda $. 我们讨论这样的参数$\lambda $的性质.
Bifurcations in Recurrent Neural Network Involving Transcendental Functions
Weinian Zhang (张伟年)
Sichuan University (四川大学)
Abstract: In this talk we investigate bifurcations of a three-node recurrent neural network, in which the transcendental function tanh(x) and its iterates are involved. Those functions make computation so comp