MATLAB: Fsolve stopped because problem appears regular

Question

I have to find the intersection point for these 2 non linear ODE's, the graph of both appears below and has an intersection point.

k=4, r=0.6

My code for fsolve is:

k=4;
r=0.6;
fnc = @(x1) [ r.*(1-(x1(1)./k)); x1(1)./(1+x1(1).^2)]
[xx,fval]=fsolve(fnc, [1 1])

When I try to use fsolve with the code above, the error says:

No solution found.

fsolve stopped because the problem appears regular as measured by the gradient,

but the vector of function values is not near zero as measured by the

value of the function tolerance.

<stopping criteria details>

These still occurs with different guess values

Answer 1

k=4;
r=0.6;
fnc = @(x1) [ r.*(1-(x1(1)./k)) ;x1(1)./(1+x1(1).^2)];
[xx,difference]=fzero(@(x1) diff(fnc(x1)), [-2,2])
xx = 0.7736
difference = -5.5511e-17
fnc(xx)
ans = 2×1
    0.4840
    0.4840