Equilibrium in a large Lotka–Volterra system with pairwise correlated interactions

Consider a Lotka–Volterra (LV) system of coupled differential equations: ẋk=xk(rk−xk+(Bx)k),x=(xk),1≤k≤n,where r=(rk) is a n×1 vector and B a n×n matrix. Assume that the interaction matrix B is random and follows the elliptic model: B=1αnA+μn1n1nT,where A=(Aij) is a n×n matrix with N(0,1) entries satisfying the following dependence structure (i) the entries Aij on and above the diagonal are i.i.d., (ii) for i更多