If your system has a subcritical bifurcation and your initial condition is too large, the solution may blow up to infinity (You can see this by considering the subcritical pitchfork bifurcation diagram and by drawing vertical arrows pointing towards the stable solutions, and away from the unstable solutions). However, the magnitude of real-world physical quantities cannot ap- proach an infinitely large value, but converges to finite numbers. This is known as saturation, and is driven by stabilizing/damping effects which become more important when the magni- tude of a quantity is larger. To model this, consider the dynamical system i = ur+2³-25. Sketch its bifurcation diagram. You can do this numerically or by hand. Can this system blow up to infinity? NB: If you want to sketch the diagram by hand, the substitution r² = y may be useful, and you may need to review how to solve inequalities with square roots. If you proceed numerically, the function roots of numpy can be useful.
If your system has a subcritical bifurcation and your initial condition is too large, the solution may blow up to infinity (You can see this by considering the subcritical pitchfork bifurcation diagram and by drawing vertical arrows pointing towards the stable solutions, and away from the unstable solutions). However, the magnitude of real-world physical quantities cannot ap- proach an infinitely large value, but converges to finite numbers. This is known as saturation, and is driven by stabilizing/damping effects which become more important when the magni- tude of a quantity is larger. To model this, consider the dynamical system i = ur+2³-25. Sketch its bifurcation diagram. You can do this numerically or by hand. Can this system blow up to infinity? NB: If you want to sketch the diagram by hand, the substitution r² = y may be useful, and you may need to review how to solve inequalities with square roots. If you proceed numerically, the function roots of numpy can be useful.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 18E
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Transcribed Image Text:2. If your system has a subcritical bifurcation and your initial condition is too large, the solution
may blow up to infinity (You can see this by considering the subcritical pitchfork bifurcation
diagram and by drawing vertical arrows pointing towards the stable solutions, and away from
the unstable solutions). However, the magnitude of real-world physical quantities cannot ap-
proach an infinitely large value, but converges to finite numbers. This is known as saturation,
and is driven by stabilizing/damping effects which become more important when the magni-
tude of a quantity is larger. To model this, consider the dynamical system i = µx+2³-25.
Sketch its bifurcation diagram. You can do this numerically or by hand. Can this system
blow up to infinity? NB: If you want to sketch the diagram by hand, the substitution r² = y
may be useful, and you may need to review how to solve inequalities with square roots. If
you proceed numerically, the function roots of numpy can be useful.
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