These equations often depend on various parame- ters, e. g. temperature, catalyst and diffusion rate, etc. Moreover, they form normally a nonlinear dissipative system, coupled by reaction among differ- ent substances.

The number and stability of solutions of a reaction-diffusion system may change abruptly with variation of the control parameters.

Cor- respondingly we see formation of patterns in the system, for example, an onset of convection and waves in the chemical reactions.

This kind of phe- nomena is called bifurcation. Nonlinearity in the system makes bifurcation take place constantly in reaction-diffusion processes.

Bifurcation in turn in- duces uncertainty in outcome of reactions.

Thus analyzing bifurcations is essential for understanding mechanism of pattern formation and nonlinear dynamics of a reaction-diffusion process.

However, an analytical bifurcation analysis is possible only for exceptional cases.

This book is devoted to nu- merical analysis of bifurcation problems in reaction-diffusion equations.

The aim is to pursue a systematic investigation of generic bifurcations and mode interactions of a dass of reaction-diffusion equations.

This is realized with a combination of three mathematical approaches: numerical methods for con- tinuation of solution curves and for detection and computation of bifurcation points; effective low dimensional modeling of bifurcation scenario and long time dynamics of reaction-diffusion equations; analysis of bifurcation sce- nario, mode-interactions and impact of boundary conditions.