Romeo and Juliet

1. Oscillations Romeo and Juliet Nullcline angles Time delays Stochastic excitation

2. Romeo and Juliet’s affections form a state space J= Love that Juliet professes for Romeo R= Love that Romeo professes for Juliet J Julietprofesses love, but Romeoprofesses hate Both profess love R Romeoprofesses love, but Julietprofesses hate Bothprofess hate

3. Juliet’s dynamics Juliet professes more and more love when Romeo expresses love J R

4. Romeo’s dynamics Romeo professes less and less love when Juliet professes love J R

5. Trajectory of Romeo and Juliet’s dynamics form a closed loop Romeo and Juliet chase each other around in a perpetual soap opera J R

6. Romeo and Juliet’s dynamics are sinusoidal J R

7. Oscillations Romeo and Juliet Nullcline angles Time delays Stochastic excitation

8. Derivatives can change sign at nullclines J R

9. Derivatives can change sign at nullclines J R

10. Crossed nullclines can support stable stars J R

11. Crossed nullclines can support stable spirals J R

12. Crossed nullclines can support closed cycles J R

13. Crossed nullclines can support unstable spirals J R

14. Oscillations Romeo and Juliet Nullcline angles Time delays Stochastic excitation

15. Time delay J R

16. Time delay J Current state Previous state R

17. Oscillations Romeo and Juliet Nullcline angles Time delays Stochastic excitation

18. Stochastic excitation J R

19. Stochastic excitation J R

20. Stochastic excitation J R