Not getting quiver to work on a 3 dimensional Non-linear system

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Philip Berg 2016-9-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/302093-not-getting-quiver-to-work-on-a-3-dimensional-non-linear-system

Hi all, and thanks you in advance for any help. I will first post how my system looks, then I will post MWE of my Quiver/Phase plane script. My issue is that the direction arrows don't correlate with simulations. I simply can't find why. Could be a MATLAB or a mathematical misconception. The script is slightly ad-hoc and I apologies if it is hard to follow, though it is commented so that each step should be fairly obvious.

function dxdt = LSQodes(~,x,p)
%Setting variables
X = x(1);
Xm = x(2);
Xstar = x(3);
%setting parameters
k1 = p(1);
k2 = p(2);
alpha = p(3);
beta = p(4);
K = p(5);
B = 1;
R = 1;
%Creating the empty vector
dxdt=zeros(3,1);
%Adding the equations
dxdt(1)=beta*B*(Xstar/(K+Xstar))-alpha*R*(X/(K+X));
dxdt(2)=alpha*R*(X/(K+X))-k1*Xm+k2*Xstar;
dxdt(3)=-beta*B*(Xstar/(K+Xstar))+k1*Xm-k2*Xstar;
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%NEW Script
function phase(p)%Takes a vector of 5 values
%Add empty figure
figure;
hold on;
%Vectors for different starting values
n=[0 10 20 30 40 60 80 100];
E=[100 80 60 40 30 20 10 0];
%Do as many simulations as starting values
i=length(n);
%Loop and plot simulations
while i>0,
 [~,dX] = ode45(@(t,x) LSQodes(t,x,p),[0 200],[100, n(i), E(i)]);
 plot(dX(:,2),dX(:,3),... %drawing x,y
     'LineWidth',2);
 plot(dX(1,2),dX(1,3),'bo',...% starting points
     'MarkerSize',10); 
 plot(dX(end,2),dX(end,3),'ks',...% ending points
     'MarkerSize',10); 
 i=i-1;
end;
%Creating even spaced matrixes with coordinates 0 to 50
x2 = linspace(0,100,15);
y2 = linspace(0,100,15);
[x3,y3] = meshgrid(x2,y2);
%Creating matrixes to hold the value of the derivative at t=0.
Xm = zeros(size(x3));
Xstar = zeros(size(x3));
%Adding the derivative of Xm and Xstar at t=0 (Yprime(1,2)&(1,3)) to the grid.
for Q = 1:numel(x3)
  [~,dx] = ode45(@(t,x) LSQodes(t,x,[p 1 1]),[0 1],[100, x3(Q), y3(Q)]);
  Xm(Q) = dx(1,2);
  Xstar(Q) = dx(1,3);
end 
%Scaling the size of the arrows in the phase field
for Z = 1:numel(x3)
Vmod = sqrt(Xm(Z)^2 + Xstar(Z)^2);
Xm(Z) = Xm(Z)/Vmod;
Xstar(Z) = Xstar(Z)/Vmod;
end
%Calling quiver to plot the arrows
quiver(x3,y3,Xm,Xstar);
xlabel('Xm');
ylabel('Xstar');
title('Phase field with simulations at different initial values');
axis tight equal;
grid;
hold off;
end