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I want to analyze a system of ODEs arising in biology of the form:

x'=a1*x*z

y'=b1*x + b2*y

z'=c1 + c2*z + c3*y*z

with x,y,z state variables and a1,b1,b2,c1,c2,c3 constant parameters.

The difference to a linear system of diffs eqs. is that two state variables are multiplied. Therefore, I think that this system falls under the nonlinear systems for which no general solution can be found analytically. Is this correct?

I could not find information on the net on systems of DEs of such a form. Can somebody send me some links about this kind of system with a multiplication of two state vars?

Thank you in advance,

Aitor