Consider the system of differential equations   where a and b are parameter with a,b>0 suppose that this system is only defined for x,y>0 a) Use the nullclines to sketch the phase portrait for this system for various a and b values b)Determine the values of a and b at which a bifurcation occurs c)Sketch the regions in the ab-plane where this system has qualitatively similar phase portraits, and describe the bifurcations that occur as the parameters cross the boundaries of these regions

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.