R(t) = Romeo's love/hate for Juliet at time t J(t) = Juliet's love/hate for Romeo at time t What happens when romantic opposites get together? A model for their romance is R = aJ j= -bR + aj, a and b positive e. If 4b = a i. Write the general solution. ii. Classify the origin.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter8: Polynomials
Section8.1: Adding And Subtracting Polynomials
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Love Affairs (Strogatz, Nonlinear Dynamics and Chaos, 1994)
Let
R(t) = Romeo's love/hate for Juliet at time t
J(t) = Juliet's love/hate for Romeo at time t
What happens when romantic opposites get together? A model for their romance is
R = aJ
j=-bR+aJ, a and b positive
e. If 4b = a
i.
Write the general solution.
ii.
Classify the origin.
iii.
Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to
consider all the qualitatively different possibilities.)
Transcribed Image Text:Love Affairs (Strogatz, Nonlinear Dynamics and Chaos, 1994) Let R(t) = Romeo's love/hate for Juliet at time t J(t) = Juliet's love/hate for Romeo at time t What happens when romantic opposites get together? A model for their romance is R = aJ j=-bR+aJ, a and b positive e. If 4b = a i. Write the general solution. ii. Classify the origin. iii. Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to consider all the qualitatively different possibilities.)
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Summarize what happens in their relationship. (Hint: Think about the eigenvectors. Be sure to consider all the qualitatively different possibilities.)

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