Dia: Dimecres 2 de juliol de 2025
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Jesús Dueñas Pamplona, Universidad de Valladolid
Títol: Dynamical Analysis of Nonautonomous Bonifacio-Lugiato Model via Concave-Convex Equation Techniques
Resum: In this talk, we present tools for studying the global dynamics of nonautonomous scalar ordinary differential equations featuring concave-convex nonlinearities, that is, nonlinearities that exhibit a transition from concavity to convexity in the state variable. These tools are applied to a simple model of superfluorescence in optics. In particular, we investigate the occurrence of uniform stability or bistability in the Bonifacio-Lugiato model by imposing constraints on the nonautonomous input used to excite the system. More generally, models governed by nonautonomous scalar equations may exhibit several transitions between concave and convex regimes, both in the state variable and over time. The theory developed here, which allows for one such change in the state variable, represents a first step toward understanding the full range of dynamical consequences arising from shape constraints on the nonautonomous vector field.
Last updated: Sun Jun 29 11:01:54 2025