Hi see below for some comments in the code on how to set the dimmensions to call the surf command.
options = odeset('RelTol',1e-6,'Stats','on');
% initial conditions
Xo = [0.5; 0.7; 2];
% choose parameters t and a
tspan = linspace(0,100);
a_vec = 0.01 : 0.005 : 0.03;
% ease the coding and readability
num_t = numel(tspan);
num_a = numel(a_vec);
num_x = numel(Xo);
% allocate output
X = zeros(num_t,num_x,num_a);
for idx = 1:num_a
% Collect all X values into a 3D matrix. Additional parameters to
% TestFunction can be added after ode45 options
[t,X(:,:,idx)] = ode45(@TestFunction,tspan,Xo,options,a_vec(idx));
end
% make sure we have the proper dimmensions before calling surf
plot_t = repmat(t,1,num_a);
plot_a = repmat(a_vec,num_t,1);
plot_x = squeeze(X(:,1,:));
% create the surf plot
figure
surf(plot_t,plot_a,plot_x)
xlabel('t values')
ylabel('a values')
zlabel('x values')
grid on
function [dx_dt]= TestFunction(~,x,a)
r=0.05; k=0.1; %a=0.02;
m=0.02; b=0.2; eta=0.06; h=1;
dx_dt(1)=r.*x(1).*(1-(x(1)./k))-a.*x(1).*x(3)+x(3).*eta;
dx_dt(2)=a.*x(1).*x(3)-m.*x(2)-b.*x(2)+h.*eta;
dx_dt(3)=b.*x(2)-eta.*x(3)-r.*x(1);
dx_dt = dx_dt';
end
