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How to Plot Phase Plane and Nullclines in MatLab?

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0

$begingroup$

I am trying to reproduce an example from the book "Nonlinear Dynamics and Chaos" by Strogatz - Example 5.2.2.

Given are:

$fracdXdt = X + Y$ and $fracdYdt = 4X - 2Y$ with initial conditions $(2,-3)$.

Solving the equations is not the problem, I just don't know how to plot the phase plane and the nullclines (where $fracdXdt = 0$ and $fracdYdt = 0$) properly in MatLab.

The outcome should be:
Fig 5.2.2

For the phase plane, I tried:

function solve
 [t,x]=ode45(@dxdt1,[-10 10],[2 -3]);

 plot(x(:,1),x(:,2))
 plot(x(:,2),x(:,1))
end

function d=dxdt1(t,x)
 d = [x(1) + x(2); 4 * x(1) - 2 * x(2)];
end

However, I only get a line.

linear-algebra matlab

share|cite|improve this question

asked Mar 28 at 16:14

cz5cz5

1

New contributor

cz5 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, I'd like to use plot if possible rather than quiver and I still have no idea how to plot the nullclines properly.
  $endgroup$
  – cz5
  Mar 28 at 17:26
  

  
  
  
  

add a comment | 

0

$begingroup$

I am trying to reproduce an example from the book "Nonlinear Dynamics and Chaos" by Strogatz - Example 5.2.2.

Given are:

$fracdXdt = X + Y$ and $fracdYdt = 4X - 2Y$ with initial conditions $(2,-3)$.

Solving the equations is not the problem, I just don't know how to plot the phase plane and the nullclines (where $fracdXdt = 0$ and $fracdYdt = 0$) properly in MatLab.

The outcome should be:
Fig 5.2.2

For the phase plane, I tried:

function solve
 [t,x]=ode45(@dxdt1,[-10 10],[2 -3]);

 plot(x(:,1),x(:,2))
 plot(x(:,2),x(:,1))
end

function d=dxdt1(t,x)
 d = [x(1) + x(2); 4 * x(1) - 2 * x(2)];
end

However, I only get a line.

linear-algebra matlab

share|cite|improve this question

asked Mar 28 at 16:14

cz5cz5

1

New contributor

cz5 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, I'd like to use plot if possible rather than quiver and I still have no idea how to plot the nullclines properly.
  $endgroup$
  – cz5
  Mar 28 at 17:26
  

  
  
  
  

add a comment | 

$begingroup$

I am trying to reproduce an example from the book "Nonlinear Dynamics and Chaos" by Strogatz - Example 5.2.2.

Given are:

$fracdXdt = X + Y$ and $fracdYdt = 4X - 2Y$ with initial conditions $(2,-3)$.

Solving the equations is not the problem, I just don't know how to plot the phase plane and the nullclines (where $fracdXdt = 0$ and $fracdYdt = 0$) properly in MatLab.

The outcome should be:
Fig 5.2.2

For the phase plane, I tried:

function solve
 [t,x]=ode45(@dxdt1,[-10 10],[2 -3]);

 plot(x(:,1),x(:,2))
 plot(x(:,2),x(:,1))
end

function d=dxdt1(t,x)
 d = [x(1) + x(2); 4 * x(1) - 2 * x(2)];
end

However, I only get a line.

linear-algebra matlab

share|cite|improve this question

asked Mar 28 at 16:14

cz5cz5

1

New contributor

cz5 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

function solve
 [t,x]=ode45(@dxdt1,[-10 10],[2 -3]);

 plot(x(:,1),x(:,2))
 plot(x(:,2),x(:,1))
end

function d=dxdt1(t,x)
 d = [x(1) + x(2); 4 * x(1) - 2 * x(2)];
end

share|cite|improve this question

asked Mar 28 at 16:14

cz5cz5

1

New contributor

cz5 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

asked Mar 28 at 16:14

cz5cz5

1

New contributor

cz5 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 28 at 16:14

cz5cz5

1

New contributor

cz5 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 28 at 16:14

cz5cz5

1