You can use plot_vector_field in a SageMath interactive just as you would use the regular plot command. Consider the Romeo-Juliet model in which each person responds only to the other's feelings: R = aJ and J = bR. (The parameters a and b can be either positive or negative.) Create an interactive that plots the vector field and lets you manipulate a and b. Then, describe how the system behaves at various parameter values. (Hint: You may find it helpful to organize your observations in a table.)

5. You can use plot_vector_fie1.d in a SageMath interactive just as you would use the regular plot command. Consider the RomeoJuliet model in which each person responds only to the other's feelings: R' = aJ and Jr = bR. (The parameters a and b can be either positive or negative.) Create an interactive that plots the vector field and lets you manipulate a and b. Then, describe how the system behaves at various parameter values. (Hint: You may nd it helpful to organize your observations in a table.)