Simple equation involving time step

I'm a beginer to MatLAb and I'm looking to practice with the ODE function with model equations. I haven't seen many tutorials on youtube for preditor prey like models. I'm working with a simple equation:

dY/dt = (Y+Z)Y

dZ/dt = (Y+Z)Z

initial at time 0: Y=1, Z=2

total time span is: t = 0:10

time step: 1

I've programmed this function:

tspan = [0 10];

y_Z0 = [1;2];

[t,y_Z] = ode15s(@fun3,tspan,y_Z0);

y=y_Z(:,1);

z=y_Z(:,2);

plot(t,y,t,z)

function dY_dZ_dT = fun3(t,y_Z)

dY_dZ_dT = zeros(2,1);

dY_dZ_dT(1) = (y_Z(1)+y_Z(2)).*y_Z(1);

dY_dZ_dT(2) = (y_Z(1)+y_Z(2)).*y_Z(2);

end

I'm not sure this is the output I'm expecting could I have help with just the general layout of the model as a template so I can practice similar equations for experience?

Thanks in advance

[Star Strider]

The problem is that that both variables increase exponentially, so after about 0.33 time units, the results become infinite. Although ‘fun3’ appears to be coded correctly with respect to ‘dY/dt’ and ‘dZ/dt’ those functions may not be correct.

tspan = [0 10];
y_Z0 = [1;2];
[t,y_Z] = ode15s(@fun3,tspan,y_Z0);

Warning: Failure at t=3.306903e-01. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (8.881784e-16) at time t.

y=y_Z(:,1);
z=y_Z(:,2);

figure
plot(t,y,t,z)

figure
semilogy(t,y,t,z)
grid

function dY_dZ_dT = fun3(t,y_Z)
    dY_dZ_dT = zeros(2,1);
    dY_dZ_dT(1) = (y_Z(1)+y_Z(2)).*y_Z(1);
    dY_dZ_dT(2) = (y_Z(1)+y_Z(2)).*y_Z(2);
end

.

[Steven Lord]

I agree with Star Strider that it seems like you implemented those equations correctly, but I don't think they're the correct equations. Take a look at the Wikipedia page for the Lotka-Volterra equations. α, β, γ, and δ in those equations are all positive and real, so each growth rate equation has one positive term and one negative term. Your equations have two positive terms.

[Chatowa]

I see thank you so the equation itself was the problem as oppsed to the programming