Example: Consider the system
Draw the nullclines and find all the equilibrium points. Use this information to determine the fate of the solutions corresponding to the following initial conditions
Answer: Note that this system is non linear. The x-nullclines are given by
We recognize the two lines x=0 (y-axis) and the line -x-y+1=0.
The y-nullclines are given by
We recognize the line y=0 (x-axis) and the circle (centered at (0,0) with radius 2). In the graph below we give the nullclines:
The equilibrium points may be obtained as the intersection between the x-nullclines and y-nullclines. There are 6 points (see the above graph). The solutions corresponding to the given points are drawn in white in the graph below:
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Author: Mohamed Amine Khamsi