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Objective: Solve and understand dynamic systems equations sets like the Lorenz equations and the Rikitake model. Rikitake proposed the following equations as a model for the self-generation of the Earth's magnetic field by large current-carrying eddies in the core. These solutions are roughly analogous to the irregular reversals of the Earth's magnetic field inferred from geological data. dx dt dy dt dt = -Vx+zy =-vy+ (z-a)x = 1- xy Assume that the time increment is 0 to 150 with increments of 0.01. For each scenario, assume at t=0, x=y=z= 5. Parta) Use a=v=0.1 for the constants. Name your solution "xA","yA","ZA". Part b) Use a=50 and v=0.1 for the constants. Name your solution "xB","yB","zB". Part c) Determine the positive strange attractors for part a, named "xstar","ystar" and "zstar" using your prior knowlege of roots. v(k² - k-²) = a x* = +k y* = ±k-l z* = vk²

Objective: Solve and understand dynamic systems equations sets like the Lorenz equations and the Rikitake model. Rikitake proposed the following equations as a model for the self-generation of the Earth's magnetic field by large current-carrying eddies in the core. These solutions are roughly analogous to the irregular reversals of the Earth's magnetic field inferred from geological data. dx dt dy dt dt = -Vx+zy =-vy+ (z-a)x = 1- xy Assume that the time increment is 0 to 150 with increments of 0.01. For each scenario, assume at t=0, x=y=z= 5. Parta) Use a=v=0.1 for the constants. Name your solution "xA","yA","ZA". Part b) Use a=50 and v=0.1 for the constants. Name your solution "xB","yB","zB". Part c) Determine the positive strange attractors for part a, named "xstar","ystar" and "zstar" using your prior knowlege of roots. v(k² - k-²) = a x* = +k y* = ±k-l z* = vk²

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Objective: Solve and understand dynamic systems equations sets like the Lorenz equations and the Rikitake model. Rikitake proposed the following equations as a model for the self-generation of the Earth's magnetic field by large current-carrying eddies in the core. These solutions are roughly analogous to the irregular reversals of the Earth's magnetic field inferred from geological data. dx dt dy dt dt = -Vx+zy =-vy+ (z-a)x = 1- xy Assume that the time increment is 0 to 150 with increments of 0.01. For each scenario, assume at t=0, x=y=z= 5. Parta) Use a=v=0.1 for the constants. Name your solution "xA","yA","ZA". Part b) Use a=50 and v=0.1 for the constants. Name your solution "xB","yB","zB". Part c) Determine the positive strange attractors for part a, named "xstar","ystar" and "zstar" using your prior knowlege of roots. v(k² - k-²) = a x* = +k y* = ±k-l z* = vk²
Transcribed Image Text:Objective: Solve and understand dynamic systems equations sets like the Lorenz equations and the Rikitake model. Rikitake proposed the following equations as a model for the self-generation of the Earth's magnetic field by large current-carrying eddies in the core. These solutions are roughly analogous to the irregular reversals of the Earth's magnetic field inferred from geological data. dx dt dy dt dt = -Vx+zy =-vy+ (z-a)x = 1- xy Assume that the time increment is 0 to 150 with increments of 0.01. For each scenario, assume at t=0, x=y=z= 5. Parta) Use a=v=0.1 for the constants. Name your solution "xA","yA","ZA". Part b) Use a=50 and v=0.1 for the constants. Name your solution "xB","yB","zB". Part c) Determine the positive strange attractors for part a, named "xstar","ystar" and "zstar" using your prior knowlege of roots. v(k² - k-²) = a x* = +k y* = ±k-l z* = vk²
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