The Brusselator is a two-species autocatalytic reaction model. In the parametrizationits positive homogeneous equilibrium is .
For the spatially homogeneous Brusselator with parameters , set . The quadrilateralis a trapping region. The four inward-pointing tests use on , on , on , and on the sloping edge.
The spatially homogeneous Brusselator has its unique positive equilibrium at . Its Jacobian there has determinant and trace . If , the equilibrium is a repeller inside the Brusselator trapping region; the Poincare-Bendixson theorem then supplies a periodic orbit.
When and have diffusivities and , respectively, and the homogeneous Brusselator equilibrium is stable, a Turing instability occurs precisely whenAt onset,
Articles by others on the same topic
The Brusselator is a mathematical model used to describe a reaction-diffusion system, particularly in the context of chemical kinetics. It was introduced by the Belgian physicists Ilya Prigogine and his collaborators in their studies of nonlinear dynamic systems. The Brusselator model is a simplified representation of autocatalytic reactions, where the autocatalytic processes lead to the emergence of complex behaviors such as oscillations and pattern formation.