Numerical Bifurcation Analysis for Reaction-Diffusion Equations

The book focuses on the numerical analysis of bifurcation problems in reaction-diffusion equations, which are essential in understanding pattern formation and nonlinear dynamics in various scientific fields. It explores how changes in parameters can lead to abrupt shifts in solutions and the emergence of complex patterns, such as convection and waves. The author employs three mathematical approaches: numerical methods for solution continuation, low-dimensional modeling of bifurcation scenarios, and analysis of boundary conditions' effects, aiming for a systematic investigation of generic bifurcations and mode interactions.