Abstract: In this talk, I present a new normal form framework for fully inhomogeneous feedforward network dynamical systems with nilpotent linear parts. We introduce the triangular $s{l}_2$-style normal form to systematically classify these systems, extending the theory to quadratic terms in arbitrary dimensions. Our approach combines classical tools such as Hermite reciprocity, transvectants, and insights from Sylvester’s work on quadratic covariants. We also formulate the orbital normal form in a general Lie algebraic setting via outer transformations, leading to a block-triangular outer normal form. Applications in 2D and 3D illustrate how this framework yields simplified models well-suited for bifurcation analysis.

 

Link Information: WEBEX MEETING

https://nationaltaiwanuniversity-ksz.my.webex.com/nationaltaiwanuniversity-ksz.my/j.php?MTID=mce3c23daa55601ccf3ec16301673da5f

Meeting number (access code): 2513 878 3687

Meeting password: RHtYX33KTR5 (74899335 when dialing from a phone or video system)

 

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