Abstract

This talk continues the discussion of pattern formation by exploring additional reaction–diffusion models and their dynamical behaviors. We will introduce the Gray–Scott, FitzHugh–Nagumo, and Barkley models, highlighting how variations in reaction kinetics and parameter values influence the types of spatial and temporal patterns that emerge.

 

The second part discusses the classification of fixed points and the role of Hopf bifurcation in the onset of oscillatory dynamics. We then turn to two canonical amplitude equations—the complex Ginzburg–Landau and Swift–Hohenberg equations—which provide simplified but powerful frameworks for describing pattern selection and stability near bifurcation thresholds. The talk concludes with remarks on numerical implementation, boundary conditions, and practical aspects of simulating spatiotemporal patterns.

 

Organizers: Chih-Hung Chang (NUK); Yu-Hau Liang (NUK)