Homework Help

Consider the nonlinear planar system I' = y(y -1)(y -2). y' = r(x+1)(a+2). . Calculate all the nullclines and the direction of the vectorfield on the nullclines. Sketch your results in the phase plane. Please clearly indicate which the r and which the y nullcline is. If you choose colours, please use the same colour scheme as in the course notes. . Calculate all steady states and the Jacobian matrix at those steady states. . According to the linearization, what can you say about the stability and kind of the steady states? What can you not say? . Use the website suggested in Chapter 18.5 of the course notes to generate a phase plane plot of the system and include enough solutions to make the dynamics visible. What can you tell from the plot that you cannot tell from the linearization? . When you look at the image obtained by the online tool, what comes to mind? Can you find a fitting name for the image