(Solved): For each of the systems in Questions (1) to (5) below, do the following: Draw the phase diagram of ...
For each of the systems in Questions (1) to (5) below, do the following: Draw the phase diagram of the system; list all the equilibrium points; determine the stability of the equilibrium points; and describe the outcome of the system from various initial points. You should consider all four quadrants of the xy-plane. (For full marks, all the following must be included, correct and clearly annotated in your phase diagram: The coordinate axes; all the isoclines; all the equilibrium points; the allowed directions of motion (both vertical and horizontal) in all the regions into which the isoclines divide the xy plane; direction of motion along isoclines, where applicable; examples of allowed trajectories in all regions and examples of trajectories crossing from a region to another, whenever such a crossing is possible. Please note that only hand-drawn phase diagrams will be marked and the use of online phase diagram plotter is prohibited.) Question 1: 20 Marks
(dx)/(dt)=-xy,(dy)/(dt)=x-7Question 2: 20 Marks
(dx)/(dt)=(x-y)(x+y),(dy)/(dt)=-y.Question 3: 20 Marks
(dx)/(dt)=7(x^(2)-x),(dy)/(dt)=7(y^(2)-y).