Abstract

This talk explores tipping points in concave and d-concave solar differential equations which are often employed in biological and ecological models. We focus on rate-induced phenomena for nonautonomous differential equations where the past and the future of the system are themselves time-dependent. We present a mathematical framework for classifying these transitions based on the internal dynamics of bounded solutions. A central finding is that finite-time Lyapunov exponents (FTLE), calculated along locally pullback attractive solutions, serve as rigorous and highly effective early-warning signals (EWS). These indicators experience a characteristic "overgrowth" as a system nears a tipping point, providing a window for intervention. Using numerical analysis of single-species population models, including those exhibiting the Allee effect, we demonstrate how these warning signals can be used to trigger control mechanisms—such as accelerating a transition in an overshooting scenario—to maintain safe operating margins and prevent population extinction.

WebEx Link

https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=m2f2e73473244968f625dd2a54c757de4

Organizer

Chueh-Hsin Chang (CCU), Jia-Yuan Dai (NTHU), Bo-Chih Huang (CCU), Chih-Chiang Huang (CCU), Yuya Tokuta (Kyoto U.), Chang-Hong Wu (NYCU)