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Exercise 1. Simulate the Romeo, Juliet and Tybalt model for c = 14 and the initial conditions R(0) both a time series and a 3-D trajectory. HINT: You'll probably want to use plotjoined=True. 5, J(0) = 5 and T(0) 1. Plot the results as %3D %3D %3D Exercise 2. Pick a set of initial conditions close to the original ones and create both trajectories and time series for them. Overlay the plots. What do you observe? Exercise 3. It can also be useful to look at the variables two at a time. Plot the trajectories of Romeo and Juliet, Romeo and Tybalt and Juliet and Tybalt. Exercise 4. In the previous exercise, it sometimes looked as if the trajectory was crossing itself. Why is this impossible? What's really going on?

Exercise 1. Simulate the Romeo, Juliet and Tybalt model for c = 14 and the initial conditions R(0) both a time series and a 3-D trajectory. HINT: You'll probably want to use plotjoined=True. 5, J(0) = 5 and T(0) 1. Plot the results as %3D %3D %3D Exercise 2. Pick a set of initial conditions close to the original ones and create both trajectories and time series for them. Overlay the plots. What do you observe? Exercise 3. It can also be useful to look at the variables two at a time. Plot the trajectories of Romeo and Juliet, Romeo and Tybalt and Juliet and Tybalt. Exercise 4. In the previous exercise, it sometimes looked as if the trajectory was crossing itself. Why is this impossible? What's really going on?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Exercise 1. Simulate the Romeo, Juliet and Tybalt model for c = the initial conditions R(0) = 5, J(0) = 5 and T(0) = 1. Plot the results as both a time series and a 3-D trajectory. HINT: You'll probably want to use plotjoined=True. 14 and Exercise 2. Pick a set of initial conditions close to the original ones and create both trajectories and time series for them. Overlay the plots. What do you observe? Exercise 3. It can also be useful to look at the variables two at a time. Plot the trajectories of Romeo and Juliet, Romeo and Tybalt and Juliet and Tybalt. Exercise 4. In the previous exercise, it sometimes looked as if the trajectory was crossing itself. Why is this impossible? What's really going on?
Transcribed Image Text:Exercise 1. Simulate the Romeo, Juliet and Tybalt model for c = the initial conditions R(0) = 5, J(0) = 5 and T(0) = 1. Plot the results as both a time series and a 3-D trajectory. HINT: You'll probably want to use plotjoined=True. 14 and Exercise 2. Pick a set of initial conditions close to the original ones and create both trajectories and time series for them. Overlay the plots. What do you observe? Exercise 3. It can also be useful to look at the variables two at a time. Plot the trajectories of Romeo and Juliet, Romeo and Tybalt and Juliet and Tybalt. Exercise 4. In the previous exercise, it sometimes looked as if the trajectory was crossing itself. Why is this impossible? What's really going on?
Romeo, Juliet and Juliet's Nurse We will now look at another system of equations. This model (with a mete- orological rather than a literary motivation) played an important role in early research on chaOs. The characters are Romeo, Juliet and Juliet's nurse. Since the nurse is involved, it makes sense to model the characters' happiness rather than their attraction to each other. With that, we have the following. Juliet really loves her nurse and wants her to be happier than Juliet herself is. So J' = s(N – J). The nurse is similarly attached to Juliet and her happiness grows in pro- portion to Juliet's. However, she's a bit of a worrywart and on her own, her happiness causes itself to decline. And she's really worried about Julet's de- veloping relationship with Romeo, so whenever their emotions are in sync, her happiness drops precipitously. Thus, N' = r.J – N – RJ. Finally, Romeo just wants his life to be simple. When Juliet and the nurse have different emotions, he finds it hard to deal with them, but he doesn't actually care if they're happy or not. Also, he's not the most emotionally stable person, so his happiness causes itself to decline, just as in the case of the nurse. So R' = JN – bR.
Transcribed Image Text:Romeo, Juliet and Juliet's Nurse We will now look at another system of equations. This model (with a mete- orological rather than a literary motivation) played an important role in early research on chaOs. The characters are Romeo, Juliet and Juliet's nurse. Since the nurse is involved, it makes sense to model the characters' happiness rather than their attraction to each other. With that, we have the following. Juliet really loves her nurse and wants her to be happier than Juliet herself is. So J' = s(N – J). The nurse is similarly attached to Juliet and her happiness grows in pro- portion to Juliet's. However, she's a bit of a worrywart and on her own, her happiness causes itself to decline. And she's really worried about Julet's de- veloping relationship with Romeo, so whenever their emotions are in sync, her happiness drops precipitously. Thus, N' = r.J – N – RJ. Finally, Romeo just wants his life to be simple. When Juliet and the nurse have different emotions, he finds it hard to deal with them, but he doesn't actually care if they're happy or not. Also, he's not the most emotionally stable person, so his happiness causes itself to decline, just as in the case of the nurse. So R' = JN – bR.
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