Phase portrait of one ode

[dedtadeas]

Hi,
I am supposed to implement one "model" of biological process from this
artical http://jigcell.cs.vt.edu/Pubs/Tyson03.pdf
I chose Negative feedback - Homeostasis.(equation and parametres are defined
in gray field on page three)
Here is what I came up with:
 
1;

#defined function for production of R
function E = E(u,v,J,K)
E = 2*u*K/(v - u + v*J + u*K + ((v-u + v*J + u*K)^2 - 4*(v-u)*u*K)^-2);
endfunction

#this variable is not set in artical - I assigned 1
R=1;
function xdot = dR(R, t)

# S is signal, which inhibits production of R
# In fact, this variable is not set in artical - inhibition of production of
R depends on R and S as well.
S = 1;

k0 = 1;
k2 = 1 ;
k3 = 0.5 ;
k4 = 1 ;
J3 = J4 = 0.01;
xdot = k0 * E(k3,k4*R,J3,J4) - k2 * S * R;
endfunction

t=linspace(0,5,100);
y = lsode("dR",R, t);
plot(t,y);

I guess, there is a problem in defining S and R values. They should stay
variable(and not become constant), but Octave returns error, if I try any
"constant-free" plotting.

Problem is that I am supposed to do phase portrait and plot it. 
1. How to make and plot phase portrait of one dimensional function? 
2. Deside which states of this system are stable.

I would be really thankfull for any answer. 

Have a nice day TAD



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