I am trying to plot this function dxdt=N0sin(omegat)x(1-x/K) to get a 3-D plot but my code does not work,where is the error?

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Avan Al-Saffar 2014-8-1

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https://ww2.mathworks.cn/matlabcentral/answers/144336-i-am-trying-to-plot-this-function-dxdt-n0-sin-omega-t-x-1-x-k-to-get-a-3-d-plot-but-my-code-does

评论： Avan Al-Saffar 2014-8-8

采纳的回答： Roger Stafford

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function RunOsciliationsky3D

N0all= 1:1:10;

N=length(N0all);

omegaall= 1:1:10;

M=length(omegaall);

Pmax=zeros(1,N);

Pmean=zeros(1,N);

Pall=[Pmax(i),Pmean(j)];

x=length(Pall);

for i=1:N

    for j =1:N
        [t,x]=ode45(@osciliation,[0 100],0.1,[],N0all(i),10,omegaall(j));
        Pall(i,j)=x;
    end
end
[N0x,omegay]=meshgrid(N0all,omegaall);
h=mesh(N0x,omegay,Pall);

1;

Note: x axis = Noall

      y axis =omegaall
      z axis = Pall, which is a matrix containing the maximum and mean values of x.

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Answer 1

Roger Stafford 2014-8-2

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It is not necessary to call on 'ode45' to solve this particular differential equation. By ordinary methods of calculus, integration of both sides of

dx/(x*(1-x/K)) = N0*sin(omega*t)*dt

will give you

x/(K-x) = C*exp(-N0/omega*cos(omega*t))

where C is a constant whose value depends on the given initial condition. All you have to do then is put in those initial conditions for x and t to solve for C, and then solve the equation for x to obtain x as an explicit function of t involving the parameters N0 and omega. With this explicit formula you should be able to do whatever plotting you have in mind.

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Roger Stafford 2014-8-7

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I will assume you have followed my reasoning via calculus to the equation

x/(K-x) = C*exp(-N0/omega*cos(omega*t))

where C is a constant parameter whose value depends on the particular initial conditions you have with x. According to your ode45 call, the value of x is to be 0.1 when t = 0. If so, that suffices to determine what C must be:

 0.1/(K-0.1) = C*exp(-N0/omega*cos(omega*0))
             = C*exp(-N0/omega)

Therefore

C = 0.1/(K-0.1)*exp(N0/omega)

which gives the equation

x/(K-x) = 0.1/(K-0.1)*exp(N0/omega*(1-cos(omega*t)))

Solving this for x gives:

 x = 0.1*K*exp(N0/omega*(1-cos(omega*t))) / ...
     (K-0.1*(1-exp(N0/omega*(1-cos(omega*t)))))
   = 0.1*K/((K-0.1)*exp(-N0/omega*(1-cos(omega*t)))+0.1)

This last equation is your explicit formula for x as a function of t, derived entirely without the use of ode45. You can do your plotting directly from this formula.

Avan Al-Saffar 2014-8-8

Thanks a lot for your explanation but actually the problem that I am asking for it is related to the meshgrid, there is something not define well at the beginning but I do not how to deal with it.

Regards

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