Cisco Webex, Online seminar
(線上演講 Cisco Webex)
From Fast-reaction to Pattern Formation: a Cross-diffusion Perspective in Population Dynamics
Cinzia Soresina (University of Trento)
Abstract: In population dynamics, cross-diffusion provides a fundamental mechanism linking fast-interaction processes to the emergence of macroscopic spatial patterns. In systems of competing species, the classical Shigesada–Kawasaki–Teramoto model was introduced to explain the appearance of stable inhomogeneous steady states characterised by spatial segregation. Remarkably, even in the absence of an activator-inhibitor reaction structure, cross-diffusion alone can drive pattern formation [1].
Beyond its phenomenological role, cross-diffusion naturally emerges from multiscale modelling. In particular, it can be derived as the fast-reaction limit of "mesoscopic" systems involving standard diffusion coupled with fast-interaction processes. This separation of time scales establishes a systematic bridge between underlying mechanisms and effective macroscopic descriptions [3], and can be exploited in a variety of ecological contexts, including predator-prey dynamics, plant ecology, and epidemiology.
As a representative case study, discussed in detail during the talk, we consider autotoxicity in plant growth dynamics, namely the negative plant-soil feedback induced by decomposed biomass affecting the plant’s own growth. The resulting macroscopic model features a cross-diffusion term that enables spatial pattern formation without explicitly introducing water as a variable [2], highlighting the structural role of cross-diffusion in ecological self-organisation. A deeper understanding of the emergence of non-homogeneous steady states is obtained through a detailed linear stability analysis combined with advanced numerical bifurcation techniques using the continuation software pde2path, complemented by direct numerical simulations.
[1] M. Breden, C. Kuehn, C. Soresina, On the influence of cross-diffusion in pattern formation, Journal of Computational Dynamics 8(2):213–240 (2021).
[2] F. Giannino, A. Iuorio, C. Soresina, Beyond water limitation in vegetation--autotoxicity patterning: a cross-diffusion model, Physica D, to appear (2025).
[3] C. Kuehn, C. Soresina, Numerical continuation for a fast-reaction system and its cross-diffusion limit, SN Partial Differential Equations and Applications 1:7 (2020).
Link Information:
Meeting number (access code): 2519 549 9915
Organizers:
Chueh-Hsin Chang (CCU), Jia-Yuan Dai (NTHU), Bo-Chih Huang (CCU), Chih-Chiang Huang (CCU), Chang-Hong Wu (NYCU) & Yuya Tokuta (Kyoto U.)
