Write and solve n dimensional ODEs

I’m trying to solve a $2n$ system of ODEs. The equations have the following form
$$frac{dx_i}{dt}=y_i-sum_j(x_j-1)$$
$$frac{dy_i}{dt}=-y_i+frac{1}{1+exp(x_i(y_i-sum_{jneq i}y_j))}$$

can anyone please assist on a convenient way in mathematica to write these kind of equations?