In this paper, we study the following biharmonic Choquard system
\(\left\{\begin{aligned}\Delta^2 u - \beta \Delta u &= \lambda_1 u + \left(I_\mu * F(u,v)\right) F_u(u,v)\quad \text{in} \mathbb{R}^4, \\[6pt]\Delta^2 v - \beta \Delta v&= \lambda_2 v + \left(I_\mu * F(u,v)\right) F_v(u,v)\quad \text{in} \mathbb{R}^4, \\[6pt]\int_{\mathbb{R}^4} |u|^2 \, dx &= a^2, \quad\int_{\mathbb{R}^4} |v|^2 \, dx = b^2, \quad u,v \in H^2(\mathbb{R}^4).\end{aligned}\right.\)
where \(\beta \geq 0,\quad a,b>0,\quad \lambda_1,\lambda_2 \in \mathbb{R},\quad I_\mu = \frac{1}{|x|^\mu}\) with μ ∈ (0, 4), Fu, Fv are partial derivatives of F and Fu, Fv have exponential critical growth in the sense of the Adams inequality. By using the minimax principle and analyzing the behavior of the least energy with respect to the masses, we prove the existence of ground state solutions for the above system.
