Question

Please help for 4 and 5. Thanks!!!

(Based on 8.3.1 from text.) The Brusselator is a simple model of a hypothetical chemical oscillator, named after the home of the scientists who proposed it. (This is a common joke played by the chemical oscillator community; there is also the "Oregonator,", "Palo Altonator," etc.) In dimensionless form, its kinetics are where a, b > 0 are parameters and x, y 2 0 are dimensionless concentrations 1. Find all the fixed points, and use the Jacobian to classify them. 2. Sketch the nullclines, and thereby construct a trapping region for the flow. 3. Show that a Hopf bifurcation occurs at some parameter value b- be, where bc is to be determined. 4. Does the limit cycle exist for b > be or b< be? Explain, using the Poincaré-Bendixson theorem 5. A possible further question would be to do some research on the (fake) reaction that generates the above differential equations and to study how the law of mass action produces them

Answer 1