文件名称:ModelforExercise1
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Exercise 1
The following differential equations describe the Van der Pol oscillator
dx/dt = μ(x − 1/3x3− y) (1)
dy/dt = (1/μ)x
Set μ = 1 and simulate the behaviour of this system. Illustrate the fact that, for non-zero values
of the initial conditions, the states of the system converge to a limit cycle. Identify the period of the trajectories on the limit cycle. Show that if μ is increased then the limit cycle becomes more elongated.
-Exercise 1
The following differential equations describe the Van der Pol oscillator
dx/dt = μ(x − 1/3x3− y) (1)
dy/dt = (1/μ)x
Set μ = 1 and simulate the behaviour of this system. Illustrate the fact that, for non-zero values
of the initial conditions, the states of the system converge to a limit cycle. Identify the period of the trajectories on the limit cycle. Show that if μ is increased then the limit cycle becomes more elongated.
The following differential equations describe the Van der Pol oscillator
dx/dt = μ(x − 1/3x3− y) (1)
dy/dt = (1/μ)x
Set μ = 1 and simulate the behaviour of this system. Illustrate the fact that, for non-zero values
of the initial conditions, the states of the system converge to a limit cycle. Identify the period of the trajectories on the limit cycle. Show that if μ is increased then the limit cycle becomes more elongated.
-Exercise 1
The following differential equations describe the Van der Pol oscillator
dx/dt = μ(x − 1/3x3− y) (1)
dy/dt = (1/μ)x
Set μ = 1 and simulate the behaviour of this system. Illustrate the fact that, for non-zero values
of the initial conditions, the states of the system converge to a limit cycle. Identify the period of the trajectories on the limit cycle. Show that if μ is increased then the limit cycle becomes more elongated.
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