Abstract

In mathematical modelling, mathematical concepts are applied to solve various problems in the field of ecology, climate change, medicine, finance, microbiology and so on. Here, we are interested in mathematical modelling in ecological systems, mainly in population dynamics. There is a growing consensus that many real-world systems have a critical threshold (i.e., tipping point), at which systems suddenly shift to a distinct state, i.e., critical transitions initiated by local bifurcation. As critical transitions can occur suddenly and are hard to manage, it is important to predict their occurrence. Although it is very tough to predict such critical transitions, various recent works suggest that generic early warning signals can detect the situation when systems approach a critical point and most of them are based on critical slowing down (CSD). In brief, CSD manifests when, as the distance to the critical point decreases, the ability of the system to recover from perturbations and return to its average trend also decreases.

On the other hand, the equations (or the parameters of the equations) are generally unknown (or difficult to estimate) in real-world systems. When we only have a data set, Empirical dynamic modelling (EDM) helps us to compute interactions in complex dynamical systems. The S-map is one of EDMs and is an equation-free approach, can reconstruct high-dimensional, time-varying interaction networks in large, nonlinear dynamical systems. Now the challenge is to find some early warning signals for EDM.

 

WebEX Link: https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m86eb2588e99d3e2a38cde280bb2ff1e0

Meeting number (access code): 2514 229 2716

Meeting password: Zu5dmhVEC42

 

 

Organizers: Feng-Bin Wang (CGU), Chang-Hong Wu (NYCU), Chang-Yuan Cheng (NKNU)