Bifurcation in a spherical reaction-diffusion system with imposed gradient
Bifurcation of steady states is studied for the system \(\partial \Phi /\partial t=\) \((D+\eta D')H\Phi +F(\Phi)+\alpha G(\Phi)\), where D, \(D'\) are (p\(\times p)\)-matrices, H is a self-adjoint operator on a Hilbert space X of functions on a d-dimensional domain, \(\Phi\) is a given function, \(\Phi \in X^ p\) and \(\eta\), \(\alpha\) are real parameters. The branching of solutions from a homogeneous state in the three-sphere is investigated, where H is a Laplacian, \(\Phi\) is a certain gradient, and F, G nonlinear functions describing some biochemical processes.
scientific article; zbMATH DE number 4161732