You likely have pre-existing X and Y variables in your workspace, which are being plotted in their entirety. Since the code shown only sets elements 1 through 9 in X and Y, any other elements that they contain will be unchanged.
To illustrate the problem:
% example random pre-existing X and Y
X = rand(100);
Y = 2*rand(100);
% Define the seeding point (x0,y0) = (2,-2)
xi= 2;
yi=-2;
% Define the time step for the integration
dt = 0.01;
% Initialize the trajectory at the seeding point
X(1)=xi;
Y(1)=yi;
for i=1:8
ui = 3*xi^2 ;
vi = 5*yi^ 2-xi.^3;
U(i)=ui;
V(i)=vi;
xi = xi +ui*dt ;
yi = yi + vi*dt ;
X(i+1) = xi; %store new positions
Y(i+1) = yi;
end
% Plot the trajectory in a new window
figure
plot(X,Y) %ploting particle trajectory
The best way to fix that is to (re-)initialize X and Y (and U and V) to be vectors of the appropriate size before your loop (i.e., pre-allocate them) so that there are no unintended elements hanging around, e.g.:
% pre-allocate vectors
N = 8;
X = zeros(1,N+1);
Y = zeros(1,N+1);
U = zeros(1,N);
V = zeros(1,N);
% Define the seeding point (x0,y0) = (2,-2)
xi= 2;
yi=-2;
% Define the time step for the integration
dt = 0.01;
% Initialize the trajectory at the seeding point
X(1)=xi;
Y(1)=yi;
for i=1:N
ui = 3*xi^2 ;
vi = 5*yi^ 2-xi.^3;
U(i)=ui;
V(i)=vi;
xi = xi +ui*dt ;
yi = yi + vi*dt ;
X(i+1) = xi; %store new positions
Y(i+1) = yi;
end
% Plot the trajectory in a new window
figure
plot(X,Y) %ploting particle trajectory
