Dia: Dimecres, 24 d'abril de 2019
Lloc: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Josep Sardanyés, Centre de Recerca Matemàtica (CRM) and Barcelona Graduate School of Mathematics (BGSMath)
Títol: Some intimacies about the saddle-node bifurcation in one and more dimensions
Resum: In this seminar we will discuss properties and dynamic behaviours tied to local bifurcations. We will specifically focus on the saddle-node (S-N) bifurcation of equilibrium points. First, we will start with a three-dimensional model for semi-arid ecosystems dynamics displaying a S-N bifurcation as the soil degradation rate increases. We will discuss the so-called ghost ecosystems, proposing a simple intervention method to avoid catastrophic extinctions for these ecosystems. Then, we will move to investigate properties of ghost phenomena due to S-N bifurcations in low-dimensional, time-continuous dynamical systems. Specifically, we will introduce analytical results on the so-called inverse-root scaling law obtained from dynamics occurring in the complex phase space which affect dynamics in the real numbers phase space. Finally, we will explain how time lags affect ghost transients properties by investigating S-N bifurcations with delay differential equations.
The results explained in this seminar are the result of joint collaborations with: Blai Vidiella, Ricard Solé, Ernest Fontich, J. Tomás Lázaro, Tomás Alarcón, Àngel Jorba, and Joan Gimeno.
Last updated: Fri Apr 19 21:12:06 2019