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I'm trying to analyze a system I found in a paper of two cells interacting, where i defines one cell, in which U inhibits V, and V inhibits U, but S gets activated by U while inhibiting it.

def system2(y,t,a_u,a_v,a_s,a_us,beta,lam):
    u1,v1,s1,u2,v2,s2=y
    
    return np.array([(lam*(a_u*(1/(1+v1**beta))+a_us*(1/(1+s_ext(s1,s2)**beta))-u1)), #u1
                     (lam*(a_v*(1/(1+u1**beta))-v1)), #v1
                     (lam*(a_s*(u1**beta/(1+u1**beta))-s1)), #s1
                     (lam*(a_u*(1/(1+v2**beta))+a_us*(1/(1+s_ext(s1,s2)**beta))-u2)), #u2
                     (lam*(a_v*(1/(1+u2**beta))-v2)), #v2
                     (lam*(a_s*(u2**beta/(1+u2**beta))-s2))]) #s2

The system looks visually like this, and s_ext is defined as

def s_ext(s1,s2):
    return (s1+s2)/2

I'm trying to plot the null clines of u1 and u2, but I can't seem to figure it out. I've solved the dynamics of the system using odeint already, but I don't know how to proceed.

After plotting the null clines, I'd like to plot the bifurcation diagram of u as the parameter a_u changes.

user11321526
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    Do you have a specific question? It’s not clear what exactly you tried to do and at which point it failed. Can you show an example of the input data for the plot and what it should look like? – mkrieger1 Jul 18 '20 at 08:51
  • Please also read this and try to follow it: [mre] – mkrieger1 Jul 18 '20 at 08:52

1 Answers1

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Writing your own code to obtain nullclines could be challenging. I came across PyDSTool to get nullclines and bifurcation diagram for your dynamical system. It may take a while to get it running because of possible version compatibility issues.

Angad Yuvraj
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  • Generally, links to or mentions of a tool or library [should be accompanied by usage notes, a specific explanation of how the linked resource is applicable to the problem, or some sample code](http://meta.stackoverflow.com/a/251605), or if possible all of the above. – DCCoder Sep 19 '20 at 17:26