To better determine values from the diagram, you can click the “show point” box and move the point around to read off coordinates from different parts of the graph.
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When $\beta= 0$, how many equilibria are there? Determine their values, rounded to the nearest integer, and their stability.
To report your answers, use the below applet to sketch the phase line for when $\beta= 0$, including equilibria and direction field. Use a solid circle for stable equilibria and an open circle for unstable equilibria. Place circles for equilibria at integer values, using the rounded values of equilibria determined from the bifurcation diagram.
Feedback from applet
equilibria:
number of equilibria:
stability of equilibria:
vector field:
Drag the slider labeled $n_e$ to specify the number of equilibria. Drag the red points to the location of the equilibria. You can click on a point to change it between open and solid. Click the segments between equilibria to show a direction field. Clicking the segment again changes the direction of the vectors.
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When $\beta= 4$, how many equilibria are there? Determine their values, rounded to the nearest integer, and their stability.
To report your answers, use the below applet to sketch the phase line for when $\beta= 4$, including equilibria and direction field. Use a solid circle for stable equilibria and an open circle for unstable equilibria. Place circles for equilibria at integer values, using the rounded values of equilibria determined from the bifurcation diagram. Follow the above instructions to change the phase line applet.
Feedback from applet
equilibria:
number of equilibria:
stability of equilibria:
vector field:
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When $\beta= 10$, how many equilibria are there? Determine their values, rounded to the nearest integer, and their stability.
To report your answers, use the below applet to sketch the phase line for when $\beta= 10$, including equilibria and direction field. Use a solid circle for stable equilibria and an open circle for unstable equilibria. Place circles for equilibria at integer values, using the rounded values of equilibria determined from the bifurcation diagram. Follow the above instructions to change the phase line applet.
Feedback from applet
equilibria:
number of equilibria:
stability of equilibria:
vector field:
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Identify any bifurcation points.
Bifurcations points are at $\beta = $
. (If there are multiple bifurcation points, separate the values of $\beta$ by commas.)