Solving ODEs with Matlab, with varying Parameters
up vote
1
down vote
favorite
Lets say I have a simple logistic equation
dx/dt = 2ax(1 - x/N)
where N is the carrying capacity, a is some growth rate, and both a and N are parameters I'd like to vary.
So what I want to do is to plot a 3D graph of my fixed point and the two parameters.
I understand how to find a fixed point of a single parameter.
Here is my sample code
function xprime = MyLogisticFunction(t,X) %% The ODE
% Parameters
N = 10 % Carrying Capacity
a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
Next my solver
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
[t,x]=ode45(@MyLogisticFunction,tspan,x0);
clf
x(end,1) % This gives me the fixed point for the parameters above.
So my real question is, how do I put a for loop across two functions, that allows me to vary a and N, so that I can plot out a 3D graph of a and N and my fixed point x*.
I've tried combining both functions into one .m file but it does not seem to work
matlab for-loop ode
asked Dec 22 '14 at 14:34
Candy Man
6911
add a comment |
up vote
1
down vote
favorite
Lets say I have a simple logistic equation
dx/dt = 2ax(1 - x/N)
where N is the carrying capacity, a is some growth rate, and both a and N are parameters I'd like to vary.
So what I want to do is to plot a 3D graph of my fixed point and the two parameters.
I understand how to find a fixed point of a single parameter.
Here is my sample code
function xprime = MyLogisticFunction(t,X) %% The ODE
% Parameters
N = 10 % Carrying Capacity
a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
Next my solver
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
[t,x]=ode45(@MyLogisticFunction,tspan,x0);
clf
x(end,1) % This gives me the fixed point for the parameters above.
So my real question is, how do I put a for loop across two functions, that allows me to vary a and N, so that I can plot out a 3D graph of a and N and my fixed point x*.
I've tried combining both functions into one .m file but it does not seem to work
matlab for-loop ode
asked Dec 22 '14 at 14:34
Candy Man
6911
What are the N and a information throughout time?
– mehmet
Dec 22 '14 at 14:41
I will vary it arbitrarily from say N = 10:1:20, a = 0.5:0.1:1.5
– Candy Man
Dec 22 '14 at 14:44
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Lets say I have a simple logistic equation
dx/dt = 2ax(1 - x/N)
where N is the carrying capacity, a is some growth rate, and both a and N are parameters I'd like to vary.
So what I want to do is to plot a 3D graph of my fixed point and the two parameters.
I understand how to find a fixed point of a single parameter.
Here is my sample code
function xprime = MyLogisticFunction(t,X) %% The ODE
% Parameters
N = 10 % Carrying Capacity
a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
Next my solver
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
[t,x]=ode45(@MyLogisticFunction,tspan,x0);
clf
x(end,1) % This gives me the fixed point for the parameters above.
So my real question is, how do I put a for loop across two functions, that allows me to vary a and N, so that I can plot out a 3D graph of a and N and my fixed point x*.
I've tried combining both functions into one .m file but it does not seem to work
matlab for-loop ode
asked Dec 22 '14 at 14:34
Candy Man
6911
Lets say I have a simple logistic equation
dx/dt = 2ax(1 - x/N)
where N is the carrying capacity, a is some growth rate, and both a and N are parameters I'd like to vary.
So what I want to do is to plot a 3D graph of my fixed point and the two parameters.
I understand how to find a fixed point of a single parameter.
Here is my sample code
function xprime = MyLogisticFunction(t,X) %% The ODE
% Parameters
N = 10 % Carrying Capacity
a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
Next my solver
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
[t,x]=ode45(@MyLogisticFunction,tspan,x0);
clf
x(end,1) % This gives me the fixed point for the parameters above.
So my real question is, how do I put a for loop across two functions, that allows me to vary a and N, so that I can plot out a 3D graph of a and N and my fixed point x*.
I've tried combining both functions into one .m file but it does not seem to work
matlab for-loop ode
matlab for-loop ode
asked Dec 22 '14 at 14:34
Candy Man
6911
asked Dec 22 '14 at 14:34
Candy Man
6911
asked Dec 22 '14 at 14:34
Candy Man
6911
asked Dec 22 '14 at 14:34
Candy Man
6911
asked Dec 22 '14 at 14:34
Candy Man
6911
6911
What are the N and a information throughout time?
– mehmet
Dec 22 '14 at 14:41
I will vary it arbitrarily from say N = 10:1:20, a = 0.5:0.1:1.5
– Candy Man
Dec 22 '14 at 14:44
add a comment |
What are the N and a information throughout time?
– mehmet
Dec 22 '14 at 14:41
I will vary it arbitrarily from say N = 10:1:20, a = 0.5:0.1:1.5
– Candy Man
Dec 22 '14 at 14:44
What are the N and a information throughout time?
– mehmet
Dec 22 '14 at 14:41
What are the N and a information throughout time?
– mehmet
Dec 22 '14 at 14:41
I will vary it arbitrarily from say N = 10:1:20, a = 0.5:0.1:1.5
– Candy Man
Dec 22 '14 at 14:44
I will vary it arbitrarily from say N = 10:1:20, a = 0.5:0.1:1.5
– Candy Man
Dec 22 '14 at 14:44
add a comment |
1 Answer
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oldest
votes
up vote
5
down vote
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You need to pass the parameters to your function:
function xprime = MyLogisticFunction(t,X,a,N) %% The ODE
% Parameters (passed as function arguments)
% N = 10 % Carrying Capacity
% a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
and then when you call the ode solver:
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
a = 0.1:0.1:1; % or whatever
N = 1:10; % or whatever
x_end = zeros(length(a),length(N));
for ii = 1:length(a)
for jj = 1:length(N)
[t,x]=ode45(@(t,X)MyLogisticFunction(t,X,a(ii),N(jj)),tspan,x0);
x_end(ii,jj) = x(end,1);
end
end
answered Dec 22 '14 at 14:44
am304
12.1k21431
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
You need to pass the parameters to your function:
function xprime = MyLogisticFunction(t,X,a,N) %% The ODE
% Parameters (passed as function arguments)
% N = 10 % Carrying Capacity
% a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
and then when you call the ode solver:
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
a = 0.1:0.1:1; % or whatever
N = 1:10; % or whatever
x_end = zeros(length(a),length(N));
for ii = 1:length(a)
for jj = 1:length(N)
[t,x]=ode45(@(t,X)MyLogisticFunction(t,X,a(ii),N(jj)),tspan,x0);
x_end(ii,jj) = x(end,1);
end
end
answered Dec 22 '14 at 14:44
am304
12.1k21431
add a comment |
up vote
5
down vote
accepted
You need to pass the parameters to your function:
function xprime = MyLogisticFunction(t,X,a,N) %% The ODE
% Parameters (passed as function arguments)
% N = 10 % Carrying Capacity
% a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
and then when you call the ode solver:
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
a = 0.1:0.1:1; % or whatever
N = 1:10; % or whatever
x_end = zeros(length(a),length(N));
for ii = 1:length(a)
for jj = 1:length(N)
[t,x]=ode45(@(t,X)MyLogisticFunction(t,X,a(ii),N(jj)),tspan,x0);
x_end(ii,jj) = x(end,1);
end
end
answered Dec 22 '14 at 14:44
am304
12.1k21431
add a comment |
up vote
5
down vote
accepted
up vote
5
down vote
accepted
You need to pass the parameters to your function:
function xprime = MyLogisticFunction(t,X,a,N) %% The ODE
% Parameters (passed as function arguments)
% N = 10 % Carrying Capacity
% a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
and then when you call the ode solver:
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
a = 0.1:0.1:1; % or whatever
N = 1:10; % or whatever
x_end = zeros(length(a),length(N));
for ii = 1:length(a)
for jj = 1:length(N)
[t,x]=ode45(@(t,X)MyLogisticFunction(t,X,a(ii),N(jj)),tspan,x0);
x_end(ii,jj) = x(end,1);
end
end
answered Dec 22 '14 at 14:44
am304
12.1k21431
You need to pass the parameters to your function:
function xprime = MyLogisticFunction(t,X,a,N) %% The ODE
% Parameters (passed as function arguments)
% N = 10 % Carrying Capacity
% a = 0.5 % Growth Rate
x1prime = 2*a*X(1)*(1 - X(1)/N );
xprime = [x1prime ]';
end
and then when you call the ode solver:
% Initial Number
x0 = 0.4;
%Time Window
tspan=[0 100];
a = 0.1:0.1:1; % or whatever
N = 1:10; % or whatever
x_end = zeros(length(a),length(N));
for ii = 1:length(a)
for jj = 1:length(N)
[t,x]=ode45(@(t,X)MyLogisticFunction(t,X,a(ii),N(jj)),tspan,x0);
x_end(ii,jj) = x(end,1);
end
end
answered Dec 22 '14 at 14:44
am304
12.1k21431
answered Dec 22 '14 at 14:44
am304
12.1k21431
answered Dec 22 '14 at 14:44
am304
12.1k21431
answered Dec 22 '14 at 14:44
am304
12.1k21431
12.1k21431
add a comment |
add a comment |
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What are the N and a information throughout time?
– mehmet
Dec 22 '14 at 14:41
I will vary it arbitrarily from say N = 10:1:20, a = 0.5:0.1:1.5
– Candy Man
Dec 22 '14 at 14:44