Stationary and oscillatory fronts in a two-component genetic regulatory network model
The authors investigate a two-component gene network model, originally used to describe the spatiotemporal patterning of the gene products in early Drosophila development and found both stable stationary and time-oscillatory fronts can occur in the reaction-diffusion system. Through reducing this system, the authors obtain explicit formula for all steady-state solutions and their linear eigenvalues. The authors also explore the range in which a monotone, stationary front is stable and show it can lose stability through a Hopf bifurcation, giving rise to oscillatory fronts. They also discuss the existence and stability of steady-state and time-oscillatory solutions with multiple extrema.
scientific article; zbMATH DE number 5791153