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How to analytically solve this ODEs?

(I doubt this system in general is solvable) but a starting point is to consider $S_A = S_B = 0$ and $W_{AB}, W_{BA}$ are constant $$ \frac{dX_A}{dt} = -X_A(1+W_{AB}X_B^n) \\ \frac{dX_B}{dt} = -X_B(1+...

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