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Let x ≥ 0, y ≥ 0, r > 1 and consider the non-linear system x′ = −x + rxy − x2 y′ = y(1 + y) (a) (2 points) Compute the Jacobian of this system. b) (4 points) The point (r−1, 1) is an equilibrium point of this system. Use supportive work to identify (r−1, 1) as sink/source, nodal/spiral, saddle point or center.

Let x ≥ 0, y ≥ 0, r > 1 and consider the non-linear system x′ = −x + rxy − x2 y′ = y(1 + y) (a) (2 points) Compute the Jacobian of this system. b) (4 points) The point (r−1, 1) is an equilibrium point of this system. Use supportive work to identify (r−1, 1) as sink/source, nodal/spiral, saddle point or center.

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  1. Let x ≥ 0 , y ≥ 0 , r > 1 and consider the non-linear system
x ′ = − x + x x y − x 2 y ′ = y ( 1 + y )
(a) (2 points) Compute the Jacobian of this system. b) (4 points) The point ( r − 1 , 1 ) is an equilibrium point of this system. Use supportive work to identify ( r − 1 , 1 ) as sink/source, nodal/spiral, saddle point or center.

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