1 romeo and juliet time delaysstochastic excitation oscillations nullcline angles
Post on 14-Dec-2015
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2
JJ = Love that Juliet professes for RomeoR = Love that Romeo professes for Juliet
Both profess love
Both profess hate Romeo professes love, but Juliet professes hate
Juliet professes love, but Romeo professes hate
Romeo and Juliet’s affections form a state space
R
4
J
𝑑 𝐽𝑑𝑡
=𝑅
𝑑𝑅𝑑𝑡
=− 𝐽
Romeo professes less and less love when Juliet professes love
R
Romeo’s dynamics
5
J
𝑑 𝐽𝑑𝑡
=𝑅
𝑑𝑅𝑑𝑡
=− 𝐽
Romeo and Juliet chase each other around in a perpetual soap opera
Trajectory of Romeo and Juliet’s dynamics form a closed loop
R
6
J
𝑑 𝐽𝑑𝑡
=𝑅
𝑑𝑅𝑑𝑡
=− 𝐽
𝑑2𝑅𝑑𝑡2
=− 𝑑 𝐽𝑑𝑡
𝑑2𝑅𝑑𝑡2
=−𝑅
𝑅=𝐴0 cos (𝑡 )
𝐽=𝐴0 sin (𝑡 )
Romeo and Juliet’s dynamics are sinusoidal
R
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