System of ODE find coefficients k

justme.h

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Joined
May 24, 2019
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9
Hello, how can i find the coefficients ki of element (2), where i =1,3 (irrationals).
dN1/dt = (a - bN2 - αN1);
dN2/dt = (-c + mN1)N2; //
a>0,b>0,α>0,c>0,m>0
With this change N1=k1x, N2=k2y,t=k3z (2) the system can be reduced to:
dx/dz=x(E - Ax - y);
dy/dz=y(-1 + x) (3);
 

A_W_7

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Joined
Jun 19, 2018
Messages
2
You can put the changes directly into initial differential equations and do some derivation.
After doing so you'll get : dx/dz = [(k3/k1)*(a - b*k2*y - (alpha)*(k1x)] .....(i) and
dy/dz = (k3/k2)*[-c + m*k1*x]*k2y = y(-c + m*k1*x)*(k3) .......(ii)
comparing (ii) with the given dy/dz, you'll get k3 = 3. and m*k1 = 1.

somehow we need to get k1.
wait, I'll get back soon.
 
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